Flow Around a Crack in a Porous Matrix and Related Problems

The equations governing plane steady-state flow in heterogeneous porous body containing cracks are presented first. Then, a general transformation lemma is presented which allows extending a particular solution obtained for a given flow problem to another configuration with different geometry, behaviour and boundary conditions. An existing potential solution in terms of discharges along the cracks, established by Liolios and Exadaktylos (J Solids Struct 43:3960–3982, 2006) for non-intersecting cracks in isotropic matrix, is extended to intersecting cracks in anisotropic matrix. The basic problem of a single straight crack in an infinite body submitted to a pressure gradient at infinity is then investigated and a closed-form solution is presented for the case of void cracks (infinite conductivity), as well as a semi-analytical solution for the case of cracks with Poiseuille type conductivity. These solutions, derived first for an isotropic matrix, are then extended to anisotropic matrices using the general transformation lemma. Finally, using the solution obtained for a single crack, a closed-form estimation of the effective permeability of micro-cracked porous materials with weak crack density is derived from a self-consistent upscaling scheme.     

Flow in a Porous Matrix with Anisotropic Structure

The flow of a viscous fluid through a porous matrix undergoing only infinitesimal deformation is described in terms of intrinsic variables, namely, the density, velocity and stress occurring in coherent elements of each material. This formulation arises naturally when macroscopic interfaces are conceptually partitioned into area fractions of fluid–fluid, fluid–solid, and solid–solid contact. Such theory has been shown to yield consistent jump conditions of mass, momentum and energy across discontinuities, either internal or an external boundary, unlike the standard mixture theory jump conditions. In the previous formulation, the matrix structure has been considered isotropic; that is, the area fractions are independent of the interface orientation. Here, that is not assumed, so in particular, the cross-section area of a continuous fluid tube depends on its orientation, which influences the directional fluxes, and in turn the directional permeability, anisotropy of the structure. The simplifications for slow viscous flow are examined, and particularly for an isotropic linearly elastic matrix in which area partitioning induces anisotropic elastic response of the mixture. A final specialization to an incompressible fluid and stationary matrix leads to potential flow, and a simple plane flow solution is presented to illustrate the effects of anisotropic permeability.     

A Kinetic Approach to the Plane Poiseuille Flow Over a Porous Matrix

The Poiseuille–Couette gas flow in a channel and the gas flow through an adjacent porous medium are considered when the governing equations are obtained via a molecular kinetic approach based on the Boltzmann equation. The mass continuity, momentum balance and energy conservation are written for the gas in the contiguous regions, whereas the behavior of the solid matrix obeys to the heat diffusion equation. Two different space scalings lead to different forms of the equations for the steady flow through the fully saturated matrix. The boundary conditions at the interface between the two domains are investigated via a matching procedure.     

Note to the Opposing Flow Regime at Mixed Convection Around a Heated Cylinder in a Porous Medium

Transport in Porous Media -     

Brinkmann Model and Double Penalization Method for the Flow Around a Porous Thin Layer

In this paper we study a penalization method used to compute the flow of a viscous fluid around a thin layer of porous material. Using a BKW method, we perform an asymptotic expansion of the solution when a little parameter, measuring the thickness of the thin layer and the inverse of the penalization coefficient, tends to zero. We compare then this numerical method with a Brinkman model for the flow around a porous thin layer.      

Solution Construction to a Class of Riemann Problems of Multiphase Flow in Porous Media

Transport in Porous Media - Fluid displacement in porous media can usually be formulated as a Riemann problem. Finding the solution to such a problem helps shed light on the dynamics of flow and...     

Analytical Solutions to Gas Flow Problems in Low Permeability Porous Media

In most of conventional porous media the flow of gas is basically controlled by the permeability and the contribution of gas flow due to gas diffusion is ignored. The diffusion effect may have significant impact on gas flow behavior, especially in low permeability porous media. In this study, a dual mechanism based on Darcy flow as well as diffusion is presented for the gas flow in homogeneous porous media. Then, a novel form of pseudo pressure function was defined. This study presents a set of novel analytical solutions developed for analyzing steady-state and transient gas flow through porous media including effective diffusion. The analytical solutions are obtained using the real gas pseudo pressure function that incorporates the effective diffusion. Furthermore, the conventional assumption was used for linearizing the gas flow equation. As application examples, the new analytical solutions have been used to design new laboratory and field testing method to determine the porous media parameters. The proposed laboratory analysis method is also used to analyze data from steady-state flow tests of three core plugs. Then, permeability (k) and effective diffusion coefficient (D _e) was determined; however, the new method allows one to analyze data from both transient and steady-state tests in various flow geometries.     

Simulation of Coupled Viscous and Porous Flow Problems

Theoretical and numerical formulations are presented for the conjugate problem involving incompressible flow and flow in a saturated porous medium. The major focus of the work is the development of a generally applicable finite element method for the simulation of both fixed interface and evolving porous interface problems. The available alternatives for coupling Darcy and non-Darcy models to the Navier-Stokes equations have been studied and evaluated in a mixed finite element framework. Questions regarding convergence of the finite element method for porous flow models have been addressed. Numerical experiments on simple flow geometries have revealed the shortcomings of both the Darcy and Brinkman models. Application of the more realistic models to practical, multidimensional, flow studies has also been demonstrated.     

Stress Distribution Around a Crack in Plane Micropolar Elasticity

In this paper we formulate the boundary value problem of plane micropolar elasticity for a domain containing a crack in Sobolev spaces and prove the existence and continuous dependence on the data of the corresponding weak solutions. We consider the cases of both finite and infinite domain and find the solutions in terms of modified single layer and modified double layer potentials with distributional densities.      

Erratum to: Unsteady Problem of Crack Propagation in the Beam Approximation

Unsteady crack propagation is studied in the beam approximation. The Euler and Timoshenko models of beam theory are used. Crack propagation is described using an energy balance equation.     

Peristaltic Flow of a Maxwell Model Through Porous Boundaries in a Porous Medium

In the present investigation we have presented the peristaltic flow of a linear Maxwell model through porous boundaries in a porous medium. The governing non-dimensional partial differential are solved in wave frame by using regular perturbation method and assumed form of solution. We have discussed the problem only for free pumping case. The effects of various physical parameters involved in the problem have been investigated and shown graphically.     

Fluid Sampling From Porous Rock to Determine Filtrate Contamination Profiles Around a Well Bore

Drilling fluid filtrate invades the pores of rock surrounding a well bore during drilling of the well, and contaminates the pore fluid originally within the rock pores. Models for the flow of contaminated pore fluid towards a sampling tool within the well bore are investigated, assuming that the filtrate has the same viscosity as the original pore fluid and that the wellbore radius is small compared to the depth of filtrate invasion. If the filtrate contamination in the fluid withdrawn from the rock is monitored as a function of the volume withdrawn, then it is shown that results can be inverted to give the radial distribution of filtrate around the well bore. A new generation of guarded sampling probes is then considered, and it is shown that the radial distribution of filtrate can be obtained by means of such a probe if the fraction of flow entering the central sampling region of the probe is small compared to that entering the concentric annular guard probe. The effects of dispersion, non-zero wellbore radius and anisotropic hydraulic permeability of the rock are also studied, and numerical simulations are used to give some indication of the effect of the ratio of the filtrate viscosity to that of the original pore fluid.     

绕裂尖白亮层的形成及其止裂作用分析

应用电磁热效应对带有裂纹的金属导体通入脉冲电流进行止裂，在裂纹尖端处熔化形成钝化焊口的同时，围绕裂尖的很小范围内形成一白亮层．分析表明：白亮层的形成对裂纹的扩展起到了屏蔽和防止应力腐蚀的作用，进一步提高了钝化止裂的效果．     

Supersonic Flow Around a V-Shaped Wing at Incidence and Yaw

A solution of the problem of the flow around a V-wing with supersonic leading edges at low angles of attack and yaw is obtained within the framework of the linear theory. Possible patterns of nonsymmetric flow around the wing are analyzed as functions of the wing geometry and the freestream velocity direction, and the ranges of angles of attack and yaw on which these patterns are realized are established. Some previously undescribed shock wave configurations are found to exist in the wing-induced conical flows.     

AC Diffusion: Transport in Porous Networks Subjected to Zero-Time-Average Advective Flow

Diffusion is a slow transport mechanism and advective transport tends to dominate in large-size systems. An alternative transport mechanism is explored herein, whereby zero time-average cyclic fluid flow is compounded with pore-scale mixing to render effective transport. Two one-dimensional cyclic flow cases are analyzed: a rigid porous network with two open boundaries subjected to cyclic flow through, and a compressible porous network with only one open boundary subjected to cyclic compression. The corresponding analytical models predict diffusion-like macroscale response and provide explicit expressions for the effective diffusion coefficients in terms of the microstructure of the porous medium and flow conditions. A parallel experimental study is conducted to corroborate analytical predictions. Results confirm the relevance of pore-scale mixing in cyclic flow as a transport mechanism in porous networks.     

Flow Adjacent to a Stretching Permeable Sheet in a Darcy–Brinkman Porous Medium

In this article, we extend the work of Chakrabarti and Gupta (1979, Quart. Appl. Math., Vol. 37, pp. 73–78), and the work of Pop and Na (1998, Mechanics Research Communications, Vol. 25, pp. 263–269) to a Darcy–Brinkman porous medium.     

管道内差压驱动机器人相关流场数值模拟研究

管道内流场对机器人的驱动力是设计管内机器人外形尺寸的基本依据,本文用数值方法计算了管道内检测机器人所受的差压驱动力。在合理提出一些基本假设后,用一阶迎风和中心差分格式离散管道内检测机器人附近流场的控制方程,用SIMPLE算法求得了不同入口流速下机器人附近的流场分布,以及流场对机器人的驱动力。结果表明雷诺数为1875时,机器人下游流场变为湍流;当雷诺数为60000时,机器人下游流场变为非定常流,出现周期性流动;计算数据还表示驱动力只与管内平均流速有关而与运行压力无关。