Numerical Simulation of Two-Phase Inertial Flow in Heterogeneous Porous Media

In this study, non-Darcy inertial two-phase incompressible and non-stationary flow in heterogeneous porous media is analyzed using numerical simulations. For the purpose, a 3D numerical tool was fully developed using a finite volume formulation, although for clarity, results are presented in 1D and 2D configurations only. Since a formalized theoretical model confirmed by experimental data is still lacking, our study is based on the widely used generalized Darcy–Forchheimer model. First, a validation is performed by comparing numerical results of the saturation front kinetics with a semi-analytical solution inspired from the Buckley–Leverett model extended to take into account inertia. Second, we highlight the importance of inertial terms on the evolution of saturation fronts as a function of a suitable Reynolds number. Saturation fields are shown to have a structure markedly different from the classical case without inertia, especially for heterogeneous media, thereby, emphasizing the necessity of a more complete model than the classical generalized Darcy’s one when inertial effects are not negligible.     

惯性平台台体结构实验模态参数识别及灵敏度分析

惯性平台台体的动态特性直接决定着惯性仪表的工作精度和可靠性，模态分析是研究机械系统动态特性的主要方法之一。在概述了实验模态分析理论的基础上，建立了某型号平台台体结构的实验模型，对其进行了实验模态分析。通过对实验结果与有限元计算结果比较，验证了有限元结果较为准确；同时针对结构存在的问题，通过灵敏度分析对结构的动力修改提出了改进意见。     

多孔介质结构对渗流惯性效应的影响规律研究

本文通过局部展开算法研究了多孔介质中排列结构对非线性渗流规律的影响．计算结果表明：规则排列结构的渗流标度律和渗流方向相关,然而非规则排列结构的渗流标度律不依赖于渗流方向而只依赖于多孔介质的几何结构．伴随着排列结构的非规则程度增强,不同方向的渗流阻力变化规律的差异性减小．当流场输运区域较为复杂且不存在较宽直通道时,渗流阻力在较宽雷诺数范围内体现出较为明显的标度律特性．周期性强非规则排列结构中不同区域大小的模型却具有相似的渗流阻力的标度律特性,同时标度律特性与孔隙度的大小相关性不大．阻力非线性标度律由多孔介质结构的不同而取值为2至3之间．     

Particle Deposition in Porous Media: Analysis of Hydrodynamic and Weak Inertial Effects

We have studied the transport and capture of non-Brownian particles in porous media, when the particles are mainly submitted to hydrodynamic and weak inertial effects. Visualization experiments have been performed using several models of porous media which consist of transparent etched networks of interconnected channels. Typical particle deposits have been observed at the corners of the grains of the porous medium. Their shape and their orientation were dependent on flow rate and on the anisotropy of the flow field. A trajectory analysis model has been applied to a porous medium made of a doubly periodic array of rectangular grains very close to the experimental model. This numerical model has been used to localize particle deposits and to determine particle capture efficiency on the grains over a range of low Stokes numbers, grain aspect ratios and flow-field anisotropy ratios. The results have been interpreted in terms of shape of particle deposits and compared successfully to experimental observations.     

Spontaneous Inertial Imbibition in Porous Media Using a Fractal Representation of Pore Wall Rugosity

Considering the separable phenomena of imbibition in complex fine porous media as a function of timescale, it is noted that there are two discrete imbibition rate regimes when expressed in the Lucas–Washburn (L–W) equation. Commonly, to account for this deviation from the single equivalent hydraulic capillary, experimentalists propose an effective contact angle change. In this work, we consider rather the general term of the Wilhelmy wetting force regarding the wetting line length, and apply a proposed increase in the liquid–solid contact line and wetting force provided by the introduction of surface meso/nanoscale structure to the pore wall roughness. An experimental surface pore wall feature size regarding the rugosity area is determined by means of capillary condensation during nitrogen gas sorption in a ground calcium carbonate tablet compact. On this nano size scale, a fractal structure of pore wall is proposed to characterize for the internal rugosity of the porous medium. Comparative models based on the Lucas–Washburn and Bosanquet inertial absorption equations, respectively, for the short timescale imbibition are constructed by applying the extended wetting line length and wetting force to the equivalent hydraulic capillary observed at the long timescale imbibition. The results comparing the models adopting the fractal structure with experimental imbibition rate suggest that the L–W equation at the short timescale cannot match experiment, but that the inertial plug flow in the Bosanquet equation matches the experimental results very well. If the fractal structure can be supported in nature, then this stresses the role of the inertial term in the initial stage of imbibition. Relaxation to a smooth-walled capillary then takes place over the longer timescale as the surface rugosity wetting is overwhelmed by the pore condensation and film flow of the liquid ahead of the bulk wetting front, and thus to a smooth walled capillary undergoing permeation viscosity-controlled flow.     

Two-Phase Inertial Flow in Homogeneous Porous Media: A Theoretical Derivation of a Macroscopic Model

The purpose of this article is to derive a macroscopic model for a certain class of inertial two-phase, incompressible, Newtonian fluid flow through homogenous porous media. Starting from the continuity and Navier–Stokes equations in each phase β and γ, the method of volume averaging is employed subjected to constraints that are explicitly provided to obtain the macroscopic mass and momentum balance equations. These constraints are on the length- and time-scales, as well as, on some quantities involving capillary, Weber and Reynolds numbers that define the class of two-phase flow under consideration. The resulting macroscopic momentum equation relates the phase-averaged pressure gradient to the filtration or Darcy velocity in a coupled nonlinear form explicitly given by

考虑气体压缩性的多孔材料渗透率和惯性系数的测定

多孔介质材料的渗透率和惯性系数是决定多孔介质中流体流动特性的重要参数，一般需要通过实验进行测定，在测定渗透律和惯性系数量，选用气体作为工作介质可以为实验带来极大的方便，然而通常的实验都将气体看作不可压缩流体，直接根据Darcy-Forchheimer定律得到这两个参数，这种近似对实验条件如样品厚度、工作压力等提出了很多要求，本文提出了在考虑气体压缩性的情况下测定渗透率和惯性系数的方法，该方法可以大大降低实验时对样品厚度、工作压力等条件的要求。本文还根据该方法对多孔材料PVF进行了渗透率和惯性系数的测定，并对测量结果进行了验证。     

Sensitivity of Intrinsic Permeability to Electrokinetic Coupling in Shaly and Clayey Porous Media

Classical Darcy’s law assumes that the intrinsic permeability of porous media is only dependent on the micro-geometrical and structural properties of the inner geometry of the medium. There are, however, numerous experimental evidences that intrinsic permeability of shaly and clayey porous material is a function of the fluid phase used in the experiments. Several pore-scale processes have been proposed to explain the observed behavior. In this study, we conduct a detailed investigation of one such mechanism, namely the electrokinetic coupling. We have developed a numerical model to simulate this process at the pore-scale, incorporating a refined model of the electrical double layer. The model is used to conduct a detailed sensitivity analysis to elucidate the relative importance of several chemical–physical parameters on the intensity of the electrokinetic coupling. We found that permeability reduction due to this mechanism is likely to occur only if the effective pore-radius is smaller than 10⁻⁶ m. We also observed that electrokinetic coupling is strongly sensitive to electrophoretic mobility, which is normally reduced in clays compared to free-water conditions. Based on these findings, we set up a suite of stochastic pore-network simulations to quantify the extent of permeability reduction. We found that only if the effective pore-radius is ranging from 5 × 10⁻⁷ m to 5 × 10⁻⁸, electrokinetic coupling can be responsible for a 5–20% reduction of the intrinsic permeability, and, therefore, this mechanism has a minor impact on situations of practical environmental or mining interest.     

On the Inertial Single Phase Flow in 2D Model Porous Media: Role of Microscopic Structural Disorder

Transport in Porous Media - In this work, single-phase incompressible laminar flow in 2D model porous media is studied and the influence of microscopic structural disorder on the flow is thoroughly...     

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.     

Co-colloidal BTEX and Microbial Transport in a Saturated Porous System: Numerical Modeling and Sensitivity Analysis

Transport in Porous Media - A large number of studies were carried out in the past to analyze the significance of colloids and microbes in remediating groundwater aquifers contaminated with...     

The Image-Based Inertial Release (IBIR) Test: A New High Strain Rate Test for Stiffness Strain-Rate Sensitivity Identification

A key limitation of current moderate and high strain rate test methods is the need for external force measurement. For high loading rate hydraulic machines, ringing in the load cell corrupts the force measurement. Similarly, the analysis of split-Hopkinson bar tests requires the assumption that the specimen is in a state of quasi-static equilibrium. Recently, image-based inertial test methods have shown that external force measurement is not required if full-field measurements are available and inertial effects are significant enough. In this case the load information is provided by the acceleration fields which are derived from full-field displacement measurements. This article describes a new image-based inertial test method that can be used for simultaneous quasi-static and high strain rate stiffness identification on the same test sample. An experimental validation of the new test method is provided using PMMA samples. A major advantage of this new test method is that it utilises a standard tensile test machine and the only specialist equipment that is required is an ultra-high speed camera.

     

Single-Slip Elastoplastic Microstructures

We consider rate-independent crystal plasticity with constrained elasticity, and state the variational formulation of the incremental problem. For generic boundary data, even the first time increment does not admit a smooth solution, and fine structures are formed. By using the tools of quasiconvexity, we obtain an explicit relaxation of the first incremental problem for the case of a single slip system. Our construction shows that laminates between two different deformation gradients are formed. Plastic deformation concentrates in one of them, the other is a purely elastic strain. For the concrete case of a simple-shear test we also obtain a completely explicit solution.     

微型惯性测量组合

本文论述了惯性测量器件和组合的发展简史、机遇，选择微型惯性测量组合牵引我国微米／纳米技术发展的依据，以及采纳的技术路线。     

捷联式惯性导航系统惯性元件的设置与可靠性

本文对惯性元件的最佳冗余设置及其在飞行器上的布局与可靠性之间的关系进行了研究，建立了相应的可靠性数学模型，探讨了３／６（Ｇ）冗余惯性元件出现第三个故障时故障的检测与识别的方法。所得结果可供惯性导航系统可靠性分析及工程上应用。     

国外微机械惯性仪表的进展

本文综述了国外微机械惯性仪表的进展；分别介绍了微硅型加速度计、微硅型陀螺仪、多功能加速度计陀螺以及微惯性测量单元的原理、结构、电路组成及性能指标；初步探讨了这类仪表的应用前景和技术发展的途径。     

Inertial instability of the Stewartson -layer

Inertial stability of a vertical shear layer (Stewartson E^1/4-layer) on the sidewall of a cylindrical tank with respect to stationary axisymmetric perturbations is inverstigated by means of a linear theory. The stability is determined by two non-dimensional parameters, the Rossby number Ro = U/2ΩL and Ekman number E = v/ΩH², where U and L = (E/4)1/4H are the characteristic velocity and width of the shear layer, respectively, Ω the angular velocity of the basic rotation, v the kinematic viscosity and H the depth of the tank.

For a given Ekman number, the flow is more unstable for larger values of the Rossby number. For E = 10⁻⁴, which is a typical value of the Ekman number realized in rotating tank experiments, the critical Rossby number Ro_c for instability and the critical axial wavenumber m_c non-dimensionalized by L⁻¹ are found to be 1.3670 and 8.97, respectively. The value of Ro_c increases and that of m_c decreases with increasing E.