A FAST NUMERICAL METHOD FOR ISOTHERMAL RESIN TRANSFER MOLD FILLING

An efficient numerical scheme is presented for simulating isothermal flow in resin transfer molding. The problem involves transient, free surface flow of an incompressible fluid into a non-deforming porous medium. A new variant of the Control Volume Finite Element (CVFE) algorithm is explained in detail. It is shown how the pressure solutions at each time step can be obtained by adding a single row and column to the Cholesky factorization of the stiffness matrix derived from a finite element formulation for the pressure field. This approach reduces the computation of a new pressure solution at each time step to essentially just two sparse matrix back-substitutions. The resulting performance improvement facilitates interactive simulation and the solution of inverse problems which require many simulations of the filling problem. The computational complexity of the calculation is bounded by O(n^2⋅5), where n is the number of nodes in the finite element mesh. A 100-fold speedup over a conventional CVFE implementation was obtained for a 2213-node problem.     

Free convection and radiation characteristics for a vertical plate embedded in a porous medium

Steady two‐dimensional free convection flow due to combined effect of radiation and convection through a porous medium bounded by a vertical infinite plate is considered. The behaviour of Darcy and non‐Darcy flow is investigated. The flow of water through different porous media under different environmental conditions is discussed. Effect of four non‐dimensional parameters, i.e. Prandtl number (Pr), modified Grashof number (G), permeability parameter (K) and radiation parameter (N) has been studied. Effect of these parameters on Nusselt number is analysed. Copyright © 2005 John Wiley & Sons, Ltd.     

流体饱和孔隙介质参数反演的模拟退火算法

本文研究了模拟退火算法在流体饱和孔隙介质参数反演中的应用。通过计算响应数据与实测响应数据的拟合将参数反问题归结为最优化问题。由于流体饱和孔隙介质运动方程的复杂性，动力响应与材料参数之间呈复杂的非线性关系，优化目标函数是非凸多峰函数。传统的梯度类优化方法一方面受局部极值的困扰难以搜索到全局最优解； 另一方面确定搜索方向须进行复杂的参数敏度分析。为克服这些困难，本文应用模拟退火算法进行了多参数反演数值模拟，模拟结果表明了模拟退火算法的可行性和稳健性。     

Automated tracking of liquid velocities in a refractive index matched porous medium

Abstract

Particle tracking velocimetry is applied to flow inside a porous column at Reynolds number Re = 28. The column is composed of refractive‐index‐matched solid and liquid materials, allowing seeding particles to be tracked in a laser‐illuminated axial slice. To complement earlier results acquired for 7 mm spheres, we conduct new experiments with larger 12 mm spheres. By improving the image acquisition and analysis, we are able to process the new experiments using fully automated algorithms instead of manual tracking. As a result, greater vector yields, more accurate velocity data, and a more complete spatial coverage are achieved.     

铝熔体在多孔介质中的渗流过程

在流体流动相似原理的基础上，提出了铝熔体在多孔介质间隙（简称多孔介质）中渗流模拟的原理和方法．设计建造了用于铝液和模拟液在外加压力下进行单向渗流的两套试验装置模拟试验揭示渗流时铝液在多孔介质中渗流的若干规律实践表明理论模型与试验吻合良好．     

铝熔体在多孔介财中的渗流过程

在流体流动相似原理的基础上，提出了铝熔体在多孔介南间隙中渗流模拟的原理和方法。设计建造了用于铝液和模拟液在外加压国下进行单向渗流的两套试验装置。     

各向异性双重孔隙介质的应力与油水两相渗流耦合理论模型

针对天然裂缝性油藏的特性,建立了描述双重孔隙介质中油水两相流体流动特性的流固耦合理论模型。该模型不仅考虑了渗透率的各向异性,而且考虑了岩石固体骨架变形的各向异性。渗流方程是依据双重孔隙的概念建立起来的,而固体骨架变形控制方程则是根据Biot 的等温、线性孔隙弹性理论建立起来的。同时,给出了横向各向同性及结构各向异性、固体材料各向同性时的双重孔隙介质的应力与油水两相渗流耦合理论模型。对该模型进行了简化,并将其简化后模型与单相流的各项同性和各向异性双重孔隙介质流固耦合理论模型进行了比较。     

恒压下树脂在双尺度多孔介质中的流动特性

基于复合材料液态模塑(LCM)工艺过程中存在半饱和区域的实验现象以及对预制体双尺度效应的逐步认识, 一些学者提出用沉浸模型来研究双尺度多孔介质的不饱和流动。通过体积均匀化方法描述了双尺度多孔介质复合材料液态模塑工艺模型的特征, 得到含有沉浸项的双尺度多孔介质的质量守恒方程, 并采用有限元法对方程进行数值求解, 通过具体算例计算了考虑双尺度效应时恒压树脂注射下不同时段的压力分布状态, 得到树脂在填充过程中流动前沿半饱和区域从出现到消失的过程, 采用不同注射压力进行模拟并比较。结果表明, 与单尺度多孔介质模型不同, 双尺度多孔介质模型更能反映实际树脂填充过程中出现的半饱和区域现象。     

Gate elements at injection locations in numerical simulations of flow through porous media: applications to mold filling

Mold filling in polymer and composite processing is usually modelled as a special case of Darcy flow in porous media. The flow pattern and the time necessary to fill the mold depend on the ‘gate’ locations where resin is injected into the closed mold. In composite manufacturing, these are commonly outlets of small tubes transporting resin from a reservoir and their diameters are several orders of magnitude smaller than the mold dimensions. Similar size issue is also encountered in other applications of flow through porous media, such as oil and water pumping and drilling. Traditionally, these inlets are modelled by pressure or flow rate boundary condition as applied at a node of the finite element mesh that represents the injection gate. The omission of the inlet radius in the model results in a mathematical singularity as the mesh gets refined. The computed pressure or flow field depends on the mesh size and does not converge to the accurate solution, as the finite element mesh is refined. It is possible to deal with this phenomenon by modelling the inlet geometry more accurately but this approach is inefficient, as it requires additional degrees of freedom and, above all, significantly complicates the modelling process if the inlet location is not fixed a priori. This paper presents a more efficient alternate solution. It uses special ‘gate’ elements embedded in the mesh around the injection locations. Instead of adjusting the geometrical modelling of the injection location, the adjacent elements use modified shape functions to accurately model pressure field in the neighbourhood of small radial inlet. The proper pressure field shape‐functions for ‘gate’ elements based on linear finite elements are derived. The implementation in an existing mold filling simulation and how the ‘gate elements’ are automatically selected is described. An example to demonstrate the use of ‘gate’ elements and convergence towards the accurate solution with mesh refinement is presented. Copyright © 2004 John Wiley & Sons, Ltd.     

A computational model for fracturing porous media

This paper presents a new computational model for simulating a fracturing process in a porous medium using the finite element method. Two independent numerical techniques are used for describing this process. The partition of unity method is used for describing the fracturing process, and the double porosity model is used for describing the resulting fluid flow. A key feature of the model is the coupling of these two independent numerical techniques, which provide the means for a better simulation of the involved physical and mechanical processes. The paper focuses on the numerical formulation of the model. The capability of the model is illustrated by means of numerical examples, which examine the behaviour of a 1D porous medium under different boundary conditions. The numerical results show that the very complicated physical and mechanical processes of the fracturing porous media can be simulated properly and efficiently. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical modelling of void inclusions in porous media

Numerical modelling of porous flow in a low‐permeability matrix with high‐permeability inclusions is a challenging task because the large ratio of permeabilities ill‐conditions the finite element system of equations. We propose a coupled model where Darcy flow is used for the porous matrix and potential flow is used for the inclusions. We discuss appropriate interface conditions in detail and show that the head drop in the inclusions can be prescribed in a very simple way. Algorithmic aspects are treated in full detail. Numerical examples show that this coupled approach precludes ill‐conditioning and is more efficient than heterogeneous Darcy flow. Copyright © 2003 John Wiley & Sons, Ltd.     

Synthesis of porous–acoustic absorbing systems by an evolutionary optimization method

Topology optimization is frequently used to design structures and acoustic systems in a large range of engineering applications. In this work, a method is proposed for maximizing the absorbing performance of acoustic panels by using a coupled finite element model and evolutionary strategies. The goal is to find the best distribution of porous material for sound absorbing panels. The absorbing performance of the porous material samples in a Kundt tube is simulated using a coupled porous–acoustic finite element model. The equivalent fluid model is used to represent the foam material. The porous material model is coupled to a wave guide using a modal superposition technique. A sensitivity number indicating the optimum locations for porous material to be removed is derived and used in a numerical hard kill scheme. The sensitivity number is used to form an evolutionary porous material optimization algorithm which is verified through examples.     

Finite analytic method for 2D steady fluid flows in heterogeneous porous media with unstructured grids

The finite analytic method (FAM) is developed to solve the 2D steady fluid flows in heterogeneous porous media with full tensor permeability on unstructured grids. The proposed FAM is constructed based upon the power‐law analytic nodal solution in the angular domain with arbitrary shape. When approaching the grid node joining the subdomains, 3 different flow patterns may exist: power‐law flow, linear flow, or the stagnant flow. Based on the nodal analytic solution, the triangle‐based FAM is proposed. Numerical examples show that the proposed numerical scheme makes the convergences much quickly than the traditional methods, typically the weighted harmonic mean method under the cell refinement. In practical applications, the grid refinement parameter n = 2 or n = 3 is recommended, and the relative error of the calculated equivalent permeability will below 4% independent of the heterogeneity. In contrast, when using the traditional numerical scheme the refinement ratio for the grid cell needs to increase dramatically to get an accurate result, especially for strong heterogeneous porous medium.     

Pore‐Scale Flow Characterization of Polymer Solutions in Microfluidic Porous Media

Polymer solutions are frequently used in enhanced oil recovery and groundwater remediation to improve the recovery of trapped nonaqueous fluids. However, applications are limited by an incomplete understanding of the flow in porous media. The tortuous pore structure imposes both shear and extension, which elongates polymers; moreover, the flow is often at large Weissenberg numbers, Wi, at which polymer elasticity in turn strongly alters the flow. This dynamic elongation can even produce flow instabilities with strong spatial and temporal fluctuations despite the low Reynolds number, Re. Unfortunately, macroscopic approaches are limited in their ability to characterize the pore‐scale flow. Thus, understanding how polymer conformations, flow dynamics, and pore geometry together determine these nontrivial flow patterns and impact macroscopic transport remains an outstanding challenge. This review describes how microfluidic tools can shed light on the physics underlying the flow of polymer solutions in porous media at high Wi and low Re. Specifically, microfluidic studies elucidate how steady and unsteady flow behavior depends on pore geometry and solution properties, and how polymer‐induced effects impact nonaqueous fluid recovery. This work thus provides new insights for polymer dynamics, non‐Newtonian fluid mechanics, and applications such as enhanced oil recovery and groundwater remediation.     

A two‐scale approach for fluid flow in fractured porous media

A two‐scale numerical model is developed for fluid flow in fractured, deforming porous media. At the microscale the flow in the cavity of a fracture is modelled as a viscous fluid. From the micromechanics of the flow in the cavity, coupling equations are derived for the momentum and the mass couplings to the equations for a fluid‐saturated porous medium, which are assumed to hold on the macroscopic scale. The finite element equations are derived for this two‐scale approach and integrated over time. By exploiting the partition‐of‐unity property of the finite element shape functions, the position and direction of the fractures is independent from the underlying discretization. The resulting discrete equations are non‐linear due to the non‐linearity of the coupling terms. A consistent linearization is given for use within a Newton–Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach, and show that faults in a deforming porous medium can have a significant effect on the local as well as on the overall flow and deformation patterns. Copyright © 2006 John Wiley & Sons, Ltd.     

泡沫型多孔介质中非达西流动特性的研究

本文通过将泡沫材料复杂结构进行几何简化，形成立方框架结构，利用简化的等效单元流道，提出一种数理模型，它既考虑固体网架表面对流体的摩擦阻力作用，也考虑网架迎着流向的迎风阻力（形状阻力），得到了在多孔介质中非达西流的压力降与流速的关系式。并用简化的框架结构导出了预估泡沫材料渗透率ｋ和Ｆ－Ｗ关系式中流速平方项的系数Ｆ。另外，还通过专用的实验装置测定了四种不同孔径泡沫陶瓷的ｋ和Ｆ。结果表明，根据所给模型理论预测的结果与实验值一致性较好，在泡沫型多孔材料的应用中能够提供流动特性的相关数据。     

A two-scale model for fluid flow in an unsaturated porous medium with cohesive cracks

A two-scale model is developed for fluid flow in a deforming, unsaturated and progressively fracturing porous medium. At the microscale, the flow in the cohesive crack is modelled using Darcy’s relation for fluid flow in a porous medium, taking into account changes in the permeability due to the progressive damage evolution inside the cohesive zone. From the micromechanics of the flow in the cavity, identities are derived that couple the local momentum and the mass balances to the governing equations for an unsaturated porous medium, which are assumed to hold on the macroscopic scale. The finite element equations are derived for this two-scale approach and integrated over time. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fractures are independent from the underlying discretization. The resulting discrete equations are nonlinear due to the cohesive crack model and the nonlinearity of the coupling terms. A consistent linearization is given for use within a Newton–Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach. The calculations indicate that the evolving cohesive cracks can have a significant influence on the fluid flow and vice versa.     

多孔介质中二氧化碳水合物生成的实验研究

以多孔介质为载体,将CO2以水合物的形式固定于海底,可以减缓温室效应。CO2水合物在多孔介质中与在纯水溶液中的生成条件有很大的不同,研究了在小型CO2气体水合物实验系统中,多孔介质中CO2水合物的生成特性,探讨了温度和压力对多孔介质中CO2水合物生成特性的影响。     

A statistical approach to strength evaluation incorporating porosity effect for porous ceramics

ABSTRACT It has not been clear whether the conventional effective volume proposed for dense brittle materials can be applied satisfactorily to the strength evaluation of porous ceramics. In the present study, a modified effective volume was proposed by incorporating the porosity effect in the statistical evaluation of strength properties of porous ceramics. The modified effective volume was derived as the conventional effective volume multiplied by a function of porosity p. In this work, a power function of (1 + p)^a was adopted as the simplest porosity function. To clarify the applicability of the modified effective volume, bending tests were conducted using smooth and notched specimens of 3 wt% MgO partially stabilised zirconia with six different porosities. The porosity dependence appeared in the relation between the conventional effective volume and the mean strength of various zirconia ceramics with different porosities. The exponent a of the porosity function was determined from experimental data obtained by using identically shaped specimens with distinct porosities, and the modified effective volume was calculated for several types of specimens used in the experiments. It was revealed that the mean strength was almost uniquely correlated with the modified effective volume independent of porosity. The experimental correlation verified the applicability of the modified effective volume to strength evaluation of porous ceramics.     

A stabilized volume‐averaging finite element method for flow in porous media and binary alloy solidification processes

A stabilized equal‐order velocity–pressure finite element algorithm is presented for the analysis of flow in porous media and in the solidification of binary alloys. The adopted governing macroscopic conservation equations of momentum, energy and species transport are derived from their microscopic counterparts using the volume‐averaging method. The analysis is performed in a single domain with a fixed numerical grid. The fluid flow scheme developed includes SUPG (streamline‐upwind/Petrov–Galerkin), PSPG (pressure stabilizing/Petrov–Galerkin) and DSPG (Darcy stabilizing/Petrov–Galerkin) stabilization terms in a variable porosity medium. For the energy and species equations a classical SUPG‐based finite element method is employed. The developed algorithms were tested extensively with bilinear elements and were shown to perform stably and with nearly quadratic convergence in high Rayleigh number flows in varying porosity media. Examples are shown in natural and double diffusive convection in porous media and in the directional solidification of a binary‐alloy. Copyright © 2004 John Wiley & Sons, Ltd.