Effect of Multi-Scale Porosity in Local Permeability Modelling of Non-Crimp Fabrics

The influence of multi-scale porosity of fibre reinforcements on local permeability is investigated, in order to determine the possibility of simplifying permeability models for more efficient permeability calculations. Unit cell models of a biaxial Non-Crimp Fabric are developed and used to investigate, whether or not the porous bundles can be excluded, when modelling the local permeability. Numerical accuracy of calculations is controlled to guarantee the quality of the results and the conclusions drawn from them. It is found that fibre bundles with high fibre density can be excluded from permeability models, while bundles with low fibre volume fractions need to be included. A new method to model the local permeability of multi-scale reinforcements is developed and verified for low fibre density in the bundles. In this method, the effects of the flow inside the fibre bundles are included through modifications of the boundary conditions of a single-scale model representing the interbundle regions. The local permeability of multi-scale reinforcements can, therefore, be calculated by models with simplified fluid domains for all fibre bundle porosities, instead of being calculated by models consisting of the entire multi-scale geometry.     

Theoretical Approach of Bubble Entrapment Through Interconnected Pores: Supplying Principle

Fiber-reinforced composite materials are often composed of fibers collected in bundles that are stitched together. During the impregnation of a fibrous preform by a liquid resin, the multiscale porous medium leads to an heterogenous flow front, and therefore bubbles may be created and entrapped. Indeed, for a wetting system, capillary pressure is higher inside bundle, due to the microspace between fibers, than outside the bundles that represent the macrospace, thus, inducing an overflow between both pore scales. Motivated by the prediction of bubble formation during fiber fabric infiltration for composite materials, we attempt to determine the bubble rate in imbibition through a simple model network with two connected capillaries, called ??Pore Doublet Model?? (PDM). Our system is composed of two parts: a first part, continuously interconnected, in which the suppling mass to the microchannel from the macrochannel occurs, and a second part connected only by nodes. To quantify the leading flow front, a theoretical model based on the supplying principle and arranged Washburn equation is proposed. This approach has been conducted for wetting liquids, Newtonian flows, incompressible fluids and pores, no inertial and gravitational forces and no dynamic contact angle. The geometrical variability (channel radius and length) and the different configuration of connections (continuous and discrete) influence the entrapped bubble rate, leading to either microbubble in the microchannel or macrobubble in the macrochannel. The outcomes can contribute to the knowledge of void formation especially during the filling of fibrous preforms and may extend the previous works on the PDM in general.     

纳米阵列中气体驱替液体的流动特征

纳米尺度下气体驱动液体流动特征在纳流控芯片及页岩气开发中具有广泛的应用前景. 利用管径规格为292.8 nm,206.2 nm,89.2 nm,67.0 nm,26.1 nm的氧化铝膜为纳米阵列,进行气驱水实验和单相气体流动实验,分析纳米尺度下气驱水流动特征. 实验表明,纳米阵列中气驱水时气体流量随驱动压力变化经历三个阶段:第一阶段流量缓慢增大,且比单相气体流量降低约一个数量级;第二阶段纳米阵列中的水被大量驱替出,流量迅速增大;第三阶段纳米阵列中的水全部被驱替出,流动特征与单相气体流动保持一致. 分析表明,气驱水第一阶段存在气液界面毛细管力的“钉扎”作用及固液界面相互作用力的影响,是产生非线性流动的主要原因;而一旦“钉扎”作用破坏,气体进入管道推动界面运动,气柱与液柱之间的毛细曲面曲率变化,毛细管力减小,气体流量急剧增大,其中毛细管力随驱替压力增大急剧变化,是造成第二阶段气体流量突变的主要原因.      

The behavior of gas-liquid interfaces in vertical tubes

Experimental studies of interface behavior when a gas flow, confined in a vertical tube, flows past a stationary body of liquid are presented. Critical conditions necessary for the interface to become unstable or break up are investigated. Specific phenomena studied include: penetration of liquid from a reservoir into the top open end of a vertical tube from which gas is emerging, flow of gas past a liquid ring maintained on the inside wall of the tube, conditions for the support of a “hanging film” on the tube wall, formation of droplets and establishment of a continuous upwards-flowing liquid film. A general mathematical formulation of this problem is presented and used to derive the set of relevant dimensionless parameters. Solutions are obtained to certain simple cases and are shown to be consistent with experiment in the limits in which one or more of the variables exerts negligible influence.     

Effect of the phase transition on intra-tow flow behavior and void formation in liquid composite molding

A model describing the microscopic isothermal flow inside a fiber bundle completely surrounded by a resin during a liquid molding process is developed. A distinguishing feature of this model is that it takes into account the liquid/vapor phase transition occurring in the gas entrapped inside the tow. In contrast to the existing void formation models which assume that the entrapped gas behaves as an ideal gas, in the present analysis, the condensation and vaporization processes inherent in the liquid/vapor system under high external pressures are simulated by using the Peng–Robinson equation of state. The numerical results show that the phase transition inside the fiber tow has strong effect on both the void dynamics and its size, thus indicating the need to account for this phenomenon in simulation of liquid composite molding processes.     

Flow Through a Two-Scale Porosity,Oriented Fibre Porous Medium

A model is described for the meso- and micro-flow through an array of oriented fibre tows with meso-channels between the tows. Axial Stokes's flow was considered in the meso-channels and Darcy's law was applied within the porous fibre tows, taking into account injection pressure and capillary pressures in both types of flow. Transverse flow transfer was modelled from the leading flow front to the lagging flow and a partial-slip boundary condition was applied at the permeable boundaries of meso-channels. Flow visualisation experiments and microstructural characterisation of laminates provided appropriate experimental data for model validation. In this, the predictions for the progress of the leading meso-flow were in excellent agreement with the experimental data. Parametric studies followed including the effects of injection pressure and meso-channel size.     

Pore-Network Modeling of Isothermal Drying in Porous Media

In this paper we present numerical results obtained with a pore-network model for the drying of porous media that accounts for various processes at the pore scale. These include mass transfer by advection and diffusion in the gas phase, viscous flow in the liquid and gas phases and capillary effects at the liquid--gas interface. We extend our work by studying the effect of capillarity-induced flow in macroscopic liquid films that form at the pore walls as the liquid--gas interface recedes. A mathematical model that accounts for the effect of films on the drying rates and phase distribution patterns is presented. It is shown that film flow is a major transport mechanism in the drying of porous materials, its effect being dominant when capillarity controls the process, which is the case in typical applications.     

Onset of flow instability in a heated capillary tube

We study the stability of flow in a heated capillary tube with an evaporating meniscus. The behavior of the vapor/liquid system, which undergoes small perturbations, is analyzed by linear approximation, in the frame of a one-dimensional model of capillary flow, with a distinct interface. The effect of the physical properties of both phases, the wall heat flux and the capillary sizes, on the flow stability is studied. The velocity, pressure and temperature oscillations in a capillary tube with a constant wall heat flux or a constant wall temperature are determined. A scenario of a possible process at small and moderate Peclet numbers corresponding to the flow in capillaries is considered. The boundaries of stability, subdividing the domains of stable and unstable flows, are outlined, and the values of geometrical and operating parameters corresponding to the transition from stable to unstable flow are estimated. It is shown that the stable capillary flow occurs at relatively small wall heat fluxes, whereas at high ones, the flow is unstable, with continuously growing velocity, pressure and temperature oscillations.     

Gas Capture in a Cavity with Porous Walls

A configuration like an upside-down bell made of porous material is considered which is initially dry but then subjected to a rising pool of liquid. As liquid touches the rim of the bell, capillary transport is initiated. Starting with a vertical wicking phase, the imbibing liquid will eventually reach the ceiling of the bell and switch over to horizonal wicking. At the end of the horizontal wicking, the cavity inside the porous bell is enclosed by liquid and the gas inside it is captured. We present a model to describe the capillary transport in the bell for both Cartesian and cylindrical geometry. As far as possible, we derive analytical solutions to the normalized differential equations that describe the problem. Beyond analytical solutions, we use Runge–Kutta shooting method to obtain numerical results. We calculate the normalized closure time to capture the gas, the amount of captured gas, and reflect on the pressure development in the gas chamber.     

复合材料内多处横向冲击损伤的光纤图像检测

基于埋设在复合材料层板中的多方位多模光纤网络的特点,提出了检测层板内部发生多处横向冲击损伤的重构算法．根据光纤损伤图像检测系统获得的图像信号,可实时、定量、直观重构并显示出层板内部各处损伤的位置和各处的损伤程度．在复合材料多点冲击损伤检测试验中,屏幕显示的损伤图示与对半透明试件同时做反向照明检测的结果相一致,证实了重构结果的正确性     

Simulations of fibre orientation in dilute suspensions with front moving in the filling process of a rectangular channel using level-set method

The simulation of fibre orientation in dilute suspension with front moving is carried out using the projection and level-set methods. The motion of fibres is described using the Jeffery equation, and the contribution of fibres to the flow is accounted for by the configuration-field method. The dilute suspension of short fibres in Newtonian fluids is considered. The governing Navier–Stokes equation for the fluid flow is solved using the projection method with finite difference scheme, while the fibre-related equations are directly solved with the Runge–Kutta method. In the present study for fibres in dilute suspension flow for injection molding, the effects of various flow and material parameters on the fibre orientation, the velocity distributions and the shapes of the leading flow front are found and discussed. Our findings indicate that the presence of fibre motion has little influence on the front shape in the ranges of fibre parameters studied at the fixed Reynolds number. Influence of changing fibre parameters only causes variation of front shape in the region near the wall, and the front shape in the central core area does not vary much with the fibre parameters. On the other hand, the fibre motion has strong influence on the distributions of the streamwise and transverse velocities in the fountain flow. Fibre motion produces strong normal stress near the wall which leads to the reduction of transversal velocity as compared to the Newtonian flow without fibres, which in turn, leads to the increased streamwise velocity near the wall. Thus, the fibre addition to the flow weakens the strength of the fountain flow. The Reynolds number has also displayed significant influence on the distribution of the streamwise velocity behind the flow front for a given fibre concentration. It is also found that the fibre orientation is not always along the direction of the velocity vector in the process of mold filling. In the region of the fountain flow, the fibre near the centreline is more oriented across the streamwise direction compared to that in the region far behind the flow front. This leads to the fact that the fibre near the centreline in the region of fountain flow is more extended along the transverse direction. As the fibre orientation in the suspension flow and the shape of the flow front have great bearing on the quality of the product made from injection molding, this study has much implications for engineering applications. These results can also be useful in other fields dealing with fibre suspensions.     

Primary and Secondary Infiltration of Wetting Liquid Sessile Droplet into Porous Medium

The infiltration of a wetting droplet into the porous medium is a two-step process referred to as primary and secondary infiltration. In the primary infiltration there is a free liquid present at the porous medium surface, and when no fluid is left on the surface, the secondary infiltration is initiated. In both situations the driving force is the capillary pressure that is influenced by the local medium heterogeneities. A capillary network model based on the micro-force balance is developed with the same formulation applied to both infiltrations. The only difference between the two is that the net liquid flow into the porous medium in the secondary infiltration is equal to zero. The primary infiltration starts as a single-phase (fully saturated) flow and may proceed as a multiphase flow. The multiphase flow emerges as the interface (flow front) becomes irregular in shape. The immobile clusters of the originally present phase can be locally formed due to entrapment. Throughout the infiltration, it was found that portions of the liquid phase can be detached from the main body of the liquid phase forming some isolated liquid ganglia that increase in number and decrease in size. The termination of the secondary infiltration occurs once the ganglia become immobile due to their reduction in size. From the transient solution, the changes in the liquid saturation and capillary pressure during the droplet infiltration are determined. The solution developed in this study is used to investigate the droplet infiltration dynamics. However, the solution can be used to study the flow in fuel cell, nano-arrays, composites, and printing.     

Viscous effects in liquid encapsulated liquid bridges

An analytical derivation of the surface deflections and the streamfunctions for the flow inside a liquid encapsulated liquid bridge has been derived using an asymptotic expansion about a small capillary number. The model assumes an initially flat and cylindrical interface under the assumption that the densities of both fluids are equal. To simplify the analysis, the top and bottom walls are assumed to be stress-free and the Reynolds number is assumed to be negligible. Flow is generated either by a moving outer wall (shear-driven flow) or by applying a temperature difference across the top and bottom walls (Marangoni-driven flow). The resulting equations show that for the shear-driven flow, as the viscosity ratio increases, the surface deflections increase monotonically. For the Marangoni-driven flow there exist values of the viscosity ratio where the surface deflections reach a minimum and then switch signs. This investigation shows that it may be possible in more realistic systems to use an outer encapsulating liquid of the proper viscosity ratio to stabilize the liquid–liquid interface during float zone crystal growth.     

Wave regimes of ascending flow of a thin layer of a viscous liquid in contact with a gas

The flow of a liquid in thin layers is one of the hydrodynamic problems of chemistry and heat engineering. The large surface area of films and their small thickness make it possible to accelerate thermal, diffusive, and chemical processes at the gas-liquid boundary.Theoretical studies of liquid flow in a vertical descending thin layer are presented in [1–4]. In this paper we study ascending wave flows of a liquid in a thin vertical layer in contact with a gas, i.e., flows in the direction opposite the action of the force due to gravity, with account for the action of the gas on the liquid surface. Such motions are encountered when oil is extracted from strata that are saturated with gas. At some distance from the stratum the oil and gas separate: the gas travels at high velocity inside the pipe, occupying a considerable portion of the pipe, and the liquid is displaced toward the pipe walls, forming a thin film. In certain cases a wave-like interface develops between the oil and gas that travels with a velocity greater than that of the liquid but less than the average gas velocity. Similar phenomena are observed in high velocity mass exchangers.We examine the effect of the gas for both laminar and turbulent flow.Studies that neglect the effect of the gas flow on the liquid show that for waves on the film surface whose lengths are considerably longer than the average thickness of the layer, the liquid motion in the film is described by boundary layer equations in which account is taken of the mass force, i.e., the force due to gravity. With some approximation, we can assume that in accounting for the effect of the gas on the liquid the liquid flow is described by these same equations.     

Water removal from porous media by gas injection: experiments and simulation

The flow of a saturated gas through a porous medium, partially occupied by a liquid phase, causes evaporation due to gas expansion. This process, referred to as flow-through drying, is important in a wide variety of natural and industrial applications, such as natural gas production, convective drying of paper, catalysts, fuel cells and membranes. X-ray imaging experiments were performed to study the flow-through drying of water-saturated porous media during gas injection. The results show that the liquid saturation profile and the rate of drying are dependent on the viscous pressure drop, the state of saturation of the gas and the capillary characteristics of the porous medium. During the injection of a completely saturated gas, drying occurs only due to gas expansion. Capillary-driven flow from regions of high saturation to regions of low saturation lead to more uniform saturation profiles. During the injection of a dry gas, a drying front develops at the inlet and propagates through the porous medium. The experimental results are compared with numerical results from a continuum model. A good agreement is found for the case of sandstone. The comparison is less satisfactory for the experiments with limestone.     

Three-Phase Flow Modelling Using Pore-Scale Capillary Pressures and Relative Permeabilities for Mixed-Wet Media at the Continuum-Scale

When regions of three-phase flow arise in an oil reservoir, each of the flow parameters, i.e. capillary pressures and relative permeabilities, are generally functions of two phase saturations and depend on the wettability state. The idea of this work is to generate consistent pore-scale based three-phase capillary pressures and relative permeabilities. These are then used as input to a 1-D continuum core- or reservoir-scale simulator. The pore-scale model comprises a bundle of cylindrical capillary tubes, which has a distribution of radii and a prescribed wettability state. Contrary to a full pore-network model, the bundle model allows us to obtain the flow functions for the saturations produced at the continuum-scale iteratively. Hence, the complex dependencies of relative permeability and capillary pressure on saturation are directly taken care of. Simulations of gas injection are performed for different initial water and oil saturations, with and without capillary pressures, to demonstrate how the wettability state, incorporated in the pore-scale based flow functions, affects the continuum-scale displacement patterns and saturation profiles. In general, wettability has a major impact on the displacements, even when capillary pressure is suppressed. Moreover, displacement paths produced at the pore-scale and at the continuum-scale models are similar, but they never completely coincide.     

内分液结构调控竖直管间歇流型建模研究

内分液流型调控管依靠微尺度网孔阻气通液的毛细力学特性,调控气液两相间歇流型以实现传热强化.基于Lockhart-Martinelli 分相模型以及Zuber-Findlay 漂移流动模型,建立描述内分液竖直管内流体动力特性的一维数学模型. 采用模型求解实验工况,计算结果与实验结果误差均在20% 以内. 计算发现,液速对流动现象起决定作用,而气速影响通过丝网的渗透程度. 在定性分析基础上,采用三角立方插值与最小二乘B 样条拟合获得了流动特性与气速、液速的定量函数关系. 据此得出结论,当Re_l < 693 7 时,一定出现第1 类工况;当Re_l > 693 7,且Re_g < 67 时,可能会出现第2 类工况,此时较低的气速会促进第2 类工况的出现. 根据建立的模型与拟合关系式可实现内分液调控管的优化设计.      

Dynamics of a liquid film sheared by a co-flowing turbulent gas

Consider the dynamics of a thin laminar liquid film flowing over an inclined wall in the presence of a co-flowing turbulent gas. The solution to the full two-phase flow problem poses substantial technical difficulties. However, by making appropriate assumptions, the solution process can be simplified and can provide valuable insights. The assumptions allow us to solve the gas and liquid problems independently. Solving for the gas flow reduces to finding perturbations to pressure and tangential stresses at the interface, influencing the liquid problem through the boundary conditions. We analyze the effect of gas flow on the liquid problem by developing an integral-boundary-layer model, which is valid up to moderate liquid Reynolds numbers. We seek solitary-wave solutions of this model under the influence of gas flow via a pseudo-arclength continuation method. Our computations demonstrate that as a general trend, the wave speed increases with increasing the gas shear and the liquid flow rate. Further insight into the problem is provided via time-dependent computations of the integral-boundary-layer model.     

Relative Permeability Analysis of Tube Bundle Models,Including Capillary Pressure

The analytical equations for calculating two-phase flow, including local capillary pressures, are developed for the bundle of parallel capillary tubes model. The flow equations that are derived were used to calculate dynamic immiscible displacements of oil by water under the constraint of a constant overall pressure drop across the tube bundle. Expressions for averaged fluid pressure gradients and total flow rates are developed, and relative permeabilities are calculated directly from the two-phase form of Darcy's law. The effects of pressure drop and viscosity ratio on the relative permeabilities are discussed. Capillary pressure as a function of water saturation was delineated for several cases and compared to a steady-state mercury-injection drainage type of capillary pressure profile. The bundle of serial tubes model (a model containing tubes whose diameters change randomly at periodic intervals along the direction of flow), including local Young-Laplace capillary pressures, was analyzed with respect to obtaining relative permeabilities and macroscopic capillary pressures. Relative permeabilities for the bundle of parallel tubes model were seen to be significantly affected by altering the overall pressure drop and the viscosity ratio; relative permeabilities for the bundle of serial tubes were seen to be relatively insensitive to viscosity ratio and pressure, and were consistently X-like in profile. This work also considers the standard Leverett (1941) type of capillary pressure versus saturation profile, where drainage of a wetting phase is completed in a step-wise steady fashion; it was delineated for both tube bundle models. Although the expected increase in capillary pressure at low wetting-phase saturation was produced, comparison of the primary-drainage capillary pressure curves with the pseudo-capillary pressure profiles, that are computed directly using the averaged pressures during the displacements, revealed inconsistencies between the two definitions of capillary pressure.     

Numerical Analysis of Coupled Heat and Mass Transfer Phenomena in Concrete at Elevated Temperatures

In this work, we present a novel methodology for incorporating the effect of fibre surface morphology on liquid water transport in polymer electrolyte membrane fuel cell gas diffusion layers (GDLs). Roughness features presented on the surface of the fibre are analysed using atomic force microscopy and are found to significantly impact the capillary pressure of liquid water pathways propagating through the GDL. A threshold capillary pressure was defined as the largest capillary pressure exhibited by the liquid water phase during the invasion of the throat. The threshold capillary pressures observed in the presence of roughness features are significantly greater than those in the absence of roughness features. Two-dimensional circumferential roughness models in cylindrical and converging-diverging throats are established, and an interfacial meniscus advancing algorithm is presented to determine the resulting threshold capillary pressures required for liquid water penetration. Revised Young–Laplace equations, which are particularly useful for pore network modeling, are suggested for calculating threshold capillary pressures that account for the effect of the roughness of throats with intrinsic contact angles greater than \(90^{\circ }\).