Unsteady Flow of an Oscillating Porous Disk and a Fluid at Infinity

An exact analytic solution of the unsteady Navier–Stokes equations is obtained for the flow caused by the non-coaxial rotations of a porous disk and a fluid at infinity. The porous disk is executing oscillations in its own plane with superimposed injection or suction. An increasing or decreasing velocity amplitude of the oscillating porous disk is also discussed. Further, it is shown that a combination of suction/injection and decreasing/increasing velocity amplitude is possible as well. In addition, the flow due to porous oscillating disk and a fluid at infinity rotating about an axis parallel to the z-axis is attempted as a second problem. Sommario. Si studia il flusso non stazionario prodotto dall'oscillazione di un disco poroso in un fluido e si fornisce una soluzione analitica delle equazioni di Navier–Stokes. Si discute l'effetto di una suzione/iniezione e di una variazione sull'ampiezza della velocità' di oscillazione. Infine si studia il flusso dovuto alle oscillazioni non coassiali di un disco poroso e di un fluido all'infinito.     

Casson Fluid Flow Due to Non-Coaxial Rotation of a Porous Disk and the Fluid at Infinity Through a Porous Medium

The flow of the Casson fluid due to non-coaxial rotation of a disk and the fluid at infinity is investigated. Partial differential equations are made dimensionless and coupled. The exact solution of the resultant nonlinear initial-boundary-value problem is solved by applying the Laplace transform. The shear stresses at the disk surface and the steady state stresses are computed. The effects of dimensionless parameters on the dimensionless primary and secondary velocities are analyzed.     

膨胀性非牛顿流体多孔介质流动的模拟分析

在表征体元尺度采用格子Boltzmann方法分析膨胀性非牛顿流体在多孔介质中的流动,基于二阶矩模型在演化方程中引入表征介质阻力的作用力项,求解描述渗流模型的广义Navier-Stokes方程．采用局部法计算形变速率张量,通过循环迭代得到非牛顿粘度和松弛时间．对多孔介质的Poiseuille流动进行分析,通过比较发现结果与孔隙尺度的解析解十分吻合,并且收敛较快,表明方法合理有效．分析了渗透率和幂律指数对速度和压力降的影响,研究结果表明,膨胀性流体的多孔介质流动不符合达西规律,压力降的增加幅度小于渗透率的减小幅度．当无量纲渗透率Da小于10-5时,流道中的速度呈现均匀分布,并且速度分布随着幂律指数的减小趋于平滑．压力降随着幂律指数的增加而增加,Da越大幂律指数对压力降的影响越明显．     

可压缩气体定常非Darcy渗流的流动分析及其应用

气体通过多孔介质的非Darcy流动具有广泛的工程应用背景，因此对多孔介质中的气体非Darcy流动进行流动分析有着非常重要的意义。然而，在通常的研究中，一般都将气体考虑为不可压缩流体，很少考虑气体的压缩性。对于高压气体以较高的速度通过多孔介质的情况，在进行流动分析时，不仅要考虑非Darcy效应，还必须考虑气体的压缩性。在本文中，对可压缩气体通过多孔介质的定常非Darcy流动进行了一维流动分析，得出了多孔介质中气体的压力分布和速度分布。还进一步给出了在高压差和高流速情况下，测定多孔介质材料渗透率和惯性系数的方法，以及多孔介质材料前后压力差与材料厚度的比Δp/L和材料有气流速度u1的解析关系。     

Thermodynamic Automaton Simulations of Fluid Flow and Diffusion in Porous Media

A thermodynamic automaton model of fluid flow in porous media is presented. The model is a nonrelativistic version of a Lorentz invariant lattice gas model constructed by Udey et al. (1998). In the previous model it was shown that the energy momentum tensor and the relativistic Boltzman equation can be rigorously derived from the collision and propagation rules. In the present paper we demonstrate that this nonrelativistic model can be used to accurately simulate well known results involving single phase flow and diffusion in porous media. The simulation results show that (1) one-phase flow simulations in porous media are consistent with Darcy's law; (2) the apparent diffusion coefficient decreases with a decrease in permeability; (3) small scale heterogeneity does not affect diffusion significantly in the cases considered.     

Generalized Macroscopic Models for Fluid Flow in Deformable Porous Media II: Numerical Results and Applications

In Part I of this study, generalized mathematical models were developed to describe the motion of fluids in porous media. The second part of this study solved the problem of fluid flow in small channels of a periodic elastic solid matrix at the pore scale numerically, and applied the volume-averaging technique to predict the macroscopic behavior of reservoirs. The numerical results demonstrated different macroscopic behavior of a porous medium due to cyclic excitation at various frequencies corresponding to the five separate characteristic macroscopic models identified in Part I. The results emphasize the need to use an appropriate model to interpret the corresponding responses of a saturated porous medium.     

Jump Conditions and Surface-Excess Quantities at a Fluid/Porous Interface: A Multi-scale Approach

We present a two-step up-scaling approach that allows to derive the jump conditions that must be imposed at the interface to account for transport phenomena in a fluid/porous domain. This general approach is first applied to a heat conduction problem to illustrate the main steps of the analysis. The heat flux and temperature jump conditions are related to surface-excess quantities, whose values depend on the interface location. Good agreement between the mesoscopic and macroscopic results are obtained, whatever the position of the interface inside the transition region. The approach is then applied to the problem of a laminar flow over a porous medium. The Beavers and Joseph relation is recovered, but only for a particular position of the interface.     

Fluid Flow Induced Internal Erosion within Porous Media: Modelling of the No Erosion Filter Test Experiment

An investigation of the potential to numerically model the no erosion filter test is performed here, where the flow through a large ensemble of particles is considered by applying minimisation of dissipation rate of energy on the ensemble that is discretised with modified Voronoi diagrams and Delaunay triangulation. Low-Reynolds number simulations are applied to each part of the Voronoi diagram using computational fluid dynamics. The mechanical friction between particles is modelled by increasing the effective viscosity for closely spaced particles. Microscopic mechanisms for successful and unsuccessful sealing of filters are obtained. The numerical results agree with previously presented experimental observations by Sherard and Dunnigan. A conformity is that the sealing starts from the end of the channel and continues outwards in the radial direction. The sealing implies that the permeability can be reduced several orders of magnitude during a test.     

Microfluidic Study on the Two-Phase Fluid Flow in Porous Media During Repetitive Drainage-Imbibition Cycles and Implications to the CAES Operation

Transport in Porous Media - Compressed air energy storage (CAES) technology has been re-emerging as a viable energy storage option to address challenges coming from the mismatch between renewable...     

Effects of Cilia Movement on Fluid Velocity: I Model of Fluid Flow due to a Moving Solid in a Porous Media Framework

Transport in Porous Media - Cilia, hair-like, organelles that are found in the respiratory tract (nasal cavity, pharynx, trachea, and bronchi) rhythmically beat to clear mucus from the airways....     

The Effect of Microstructure on Models for the Flow of a Bingham Fluid in Porous Media: One-Dimensional Flows

The Buckingham–Reiner models for the one-dimensional flow of a Bingham fluid along a uniform pipe or channel are well-known, but are modified here to cover much more general one-dimensional configurations. These include selections of channels with different widths, and five different probability density functions describing distributions of channel widths. It is found that the manner in which breakthrough occurs at the threshold pressure gradient depends very strongly on the type of distribution of pores and that a pseudo-threshold pressure gradient, which might be inferred from measurements of flow at relatively high pressure gradients, may be more than twice the magnitude of the true threshold gradient.     

On Vibration-Induced Fluid and Particle Motion in Unconsolidated Porous Media: Observations and Dimensional Scaling Analysis

Vibrations are omnipresent. They arise in laboratories, pilot plants, industrial facilities and in natural settings from manmade or natural sources. Their impacts on fluid behavior from movement to interfacial mass transfer and reaction outcomes remain poorly understood. In this work, a scaling approach is developed and applied to the assessment of vibration-induced phenomena in bubble-fluid-unconsolidated solid media systems. The impacts of the interactions among these phenomena are illustrated. The analysis is supported by experimental measurements related to the motion of single-phase liquids, two-phase liquids and liquid + dispersed gas bubbles within unconsolidated porous media, observed using a UV fluorescence technique, at 50 and 500 Hz in a dynamic pressure view cell. Transmitted pressures with peak-to-peak amplitudes of 50 kPa are measured after flowing through a 4 Darcy bed of \(210\,\upmu \hbox {m}\) D50 sand particles. When bubbles are present in vibrating systems, bubble-related phenomena are shown to dominate all other effects. Bubbles far from or near resonant size, or formed and grown to resonant size disrupt interfacial forces holding non-wetting phases in unconsolidated media; cause media compaction and media and liquid motion; and mixing of fluids. These observations, described and discussed on the basis of high-resolution still and video imagery, are placed into context using dimensional analysis. The application of vibration to bubbles in porous media allows for potential applications such as improved well connectivity, gas mass transfer and particle or immiscible fluid delivery/removal. This paper is in Robert Stewart’s PhD thesis, University of Alberta, 2016.     

Derivation of Matching Conditions at the Contact Surface Between Fluid-Saturated Porous Solid and Bulk Fluid

The compatibility conditions matching macroscopic mechanical fields at the contact surface between fluid-saturated porous solid and adjacent bulk fluid are considered. Special attention is paid to the derivation of conditions for tangential components of the fluid flow velocities and to the verification of validity of the condition postulated by Beavers and Joseph. It has been shown that at the contact surface between two media, a dissipation of mechanical energy due to the fluid viscosity does exist and thus the form of a dissipation function has been proposed. It has been proven that this relation determines the form of two linear compatibility conditions derived for the tangential components of the relative fluid velocities and that these conditions describe the experimental results more precisely than the condition postulated by Beavers and Joseph.     

Inertial and Second Grade Effects on Macroscopic Equations for the Flow of a Fluid in a Porous Medium

Homogenization techniques are used to upscale from pore to laboratory or field scale viscous and second grade nonNewtonian flow in a porous medium. Nonlinear forms of Darcy's law are obtained and analysed under a series of symmetry properties. The general case of displacement of one of these fluids by another with different properties is considered and a linear stability analysis is performed.     

Analytical Study of Fluid Flow and Heat Transfer during Forced Convection in a Composite Channel Partly Filled with a Brinkman–Forchheimer Porous Medium

In this paper, the problem of fully developed forced convection in a parallel-plate channel partly filled with a homogeneous porous material is considered. The porous material is attached to the walls of the channel, while the center of the channel is occupied by clear fluid. The flow in the porous material is described by a nonlinear Brinkman–Forchheimer-extended Darcy equation. Utilizing the boundary-layer approach, analytical solutions for the flow velocity, the temperature distribution, as well as for the Nusselt number are obtained. Dependence of the Nusselt number on several parameters of the problem is extensively investigated.     

Free Flow at the Interface of Porous Surfaces: A Generalization of the Taylor Brush Configuration

A solution to the problem of shallow laminar water flow above a porous surface is essential when modeling phenomena such as erosion, resuspension, and mass transfer between the porous media and the flow above it. Previous studies proposed theoretical, experimental, and numerical insight with no single general solution to the problem. Many studies have used the Brinkman equation, while others showed that it does not represent the actual interface flow conditions. In this paper we show that the interface macroscopic velocity can be accurately modeled by introducing a modification to the Brinkman equation. A moving average approach was proved to be successful when choosing the correct representative elementary volume and comparing the macroscopic solution with the average microscopic flow. As the size of the representative elementary volume was found to be equal to the product of the square root of the permeability and an exponential function of the porosity, a general solution is now available for any brush configuration. Given the properties of the porous media (porosity and permeability), the flow height and its driving force, a complete macroscopic solution of the interface flow is obtained.     

Linear Instability Analysis of a Suspension of Oxytactic Bacteria in Superimposed Fluid and Porous Layers

The purpose of this paper is to perform a pioneering investigation of the stability of bioconvection of oxytactic bacteria in superimposed fluid and porous layers. A dilute suspension of oxytactic bacteria in a shallow system that consists of superimposed fluid and porous layers is considered. A linear instability analysis of this problem is performed and the Galerkin method is utilized to solve the eigenvalue problem. The analysis leads to an equation for the critical Rayleigh number.*Author for correspondence: Tel.: +1-919-515-5292; Fax: +1-919-515-7968; e-mail: avkuznet@eos.ncsu.edu