A boundary element simulation of compression mold filling

This paper presents the development of the boundary element equations for the compression molding process of isothermal Newtonian fluids. It shows the numerical implementation of the boundary element equations and presents a simple method of carrying out the domain integral present in the governing equations. The results and accuracy of a boundary element simulation are discussed, and the numerical results compared to experimental values.     

Multi-scale finite element modelling of laminar steady flow through highly permeable porous media

The Brinkman equation is used to model the isothermal flow of Newtonian fluids in a highly permeable porous medium between two parallel plates. Due to the multi-scale nature of flow regimes represented by the Brinkman equation, the standard Galerkin method requires excessive mesh refinement to achieve stable and accurate results. To avoid this, a residual free method is used to derive appropriate bubble functions for inclusion in the finite element discretisations. It is shown that by using bubble enriched shape functions the standard Galerkin method can yield accurate and stable solutions for multi-scale problems. In this paper the performances of the third and fifth order bubble functions used in conjunction with bilinear Lagrangian elements to solve the Brinkman equation via a penalty finite element scheme, are reported.     

Prediction of the effective diffusion coefficient in random porous media using the finite element method

A finite-element-based method is presented for evaluating the effective gas diffusion coefficient of porous solids. Using this method, the 3-D micro-scale geometries of the porous solids are constructed under the ANSYS platform by the parametric code; the relation between effective gas diffusivity and micro-scale features of random-distributed porous solids is established. The results show that in random-distributed pore media, there is a percolation threshold ε _p, and this percolation threshold decreases with increasing coordination number of the pore network. The relationship between the effective diffusivity and porosity is strongly nonlinear when the porosity, ε, is less than a certain value ε _L ; for ε > ε _L , the relationship becomes quasi-linear. This dividing point ε _L decreases with increasing coordination number. The larger the coordination number of the pore network, the higher the effective gas diffusivity. Based on the simulation results and observations, a formula relating the effective diffusion coefficient with porosity is proposed.     

A unified approach to determine principal permeability of fibrous porous media

This paper presents a unified approach (UA) to determining permeability in liquid composite molding. The UA applies both to the channel flow and the radial flow experiment and it unifies the data processing of almost all known permeability measurement methods. It permits principal permeability to be calculated from experimental measurements which are carried out in an arbitrary co-ordinate system. This paper describes the UA and its main features. Further, the UA is applied to a number of experimental results for radial flow and channel flow measurements to demonstrate its validity. In addition, the algorithms of current permeability measurement methods are classified according to the UA, and, where necessary, differences are discussed. Some data processing algorithms were found to contain weaknesses or shortcomings.     

Evaluation of effective thermal conductivity for carbon nanotube/polymer composites using control volume finite element method

Effective thermal conductivity of the polymeric composites filled with carbon nanotubes (CNTs) is predicted by using the asymptotic expansion homogenization technique (AEH), which makes it possible to localize and homogenize a heterogeneous medium. In the present study, CNT embedded epoxy composites are taken into account as the heterogeneous system. The representative volume element (RVE) employed in the homogenization process is constructed by assuming that the CNTs are dispersed homogeneously in the polymer matrix. It is presumed that the RVE contains a single CNT and that there is no direct interaction between neighboring CNTs. The dispersion state of CNTs in the composites is morphologically characterized by the field emission scanning electronic microscope (FESEM). In order to consider the orientation state of CNTs, the bounding approach is adopted by using the orientation tensor. It is found that the numerically homogenized thermal conductivity is higher than that obtained by the analytic model. Predicted conductivities are also compared with experimental results as well as analytic results. The homogenization technique yields the effective thermal conductivity accordant with experimental results. In the case that a heterogeneous material has anisotropic properties or geometrical complexity, the homogenization technique is an efficient method to obtain averaged material properties equivalent to those of the real heterogeneous medium.     

Transient diffusion with n-order irreversible chemical reaction: A finite element approach

Using the GALERKIN procedure, a finite element approximation of the non linear equation describing transient diffusion with irreversible chemical reactThe outlined method, accounting for a variety of complex geometrical domains and boundary conditions, is applicable to a wide variety of problems in wh     

A micromechanically motivated finite element approach to the fracture toughness of silicon nitride

Silicon nitride is often used, when high fracture toughness and strength is needed. For a safe and economic structural design with this material, a prediction of its resistance against thermal and mechanical loads is important. The finite element method together with a continuum damage mechanics model allows for such calculations. The parameters of the suggested model have been adjusted to three-dimensional micromechanical finite element simulations, which include models for the microstructure, the thermoelasticity and the fracture. The material model is used for four-point bend test simulations. The results are compared to recent experiments.     

A new approach to anisotropic conductive networks

A liquid-crystalline bifunctional monomer with two different reactive moieties was prepared by esterification of 4-(6-(acryloyloxy)hexyloxy)benzoic acid and 4-[11-(3-thienyl)undecyloxy]-4′-hydroxybiphenyl. A mesogenic side-chain polyacrylate containing a thienyl moiety at the extremity of its side chain was obtained by radical polymerization of the monomer. The subsequent reaction of the thienyl moiety with FeCl₃ leads to the formation of an anisotropic network with a poly(thiophene) unit. Received: 17 January 1997/Accepted: 5 March 1997     

A hybrid finite element/finite difference algorithm for compressible/incompressible viscoelastic liquids

A unified formulation is proposed for modelling compressible/incompressible viscoelastic liquids. The pure hyperbolic nature of the model overcomes some of the drawbacks of available models. The most important of these drawbacks is the mixed nature of the resulting systems of equations, with the subsequent consequence of having no general numerical algorithm for the solution. A new non‐dimensionalisation procedure is adopted. A hybrid least‐squares finite element/finite difference scheme coupled with a Newton‐Raphson's algorithm is used to solve the resulting system of equations. The method is used to predict the velocity and stress fields for different Weissenberg numbers for two benchmark problems.     

Adaptive model following control of the mold filling process in an injection molding machine

This paper is concerned with the practical application of the adaptive model following control (AMFC) theory on the cavity pressure control of the mold filling process in an injection molding machine. The experimental results indicate that the AMFC technique based on the modified Popov-Landau method is very useful for the cavity pressure control. Two kinds of control algorithms are implemented on a 16 bit microcomputer to control the cavity pressure. The results also show that the AMFC algorithm is superior to the classical PI control in this system when the acrylonitrile-butadiene-stryrene (ABS) is injected into a test specimen mold which is designed according to the ASTM code.     

A study on the mold filling process in resin transfer molding

A numerical simulation of the mold filling process during resin transfer molding (RTM) was performed using the boundary element method (BEM). Experimental verification was also done. Darcy's law for anisotropic porous media was employed along with mass conservation to construct the governing differential equation. The resulting potential problem was solved with the boundary element technique. As the calculation domain changed due to the proceeding resin front, boundary nodes were rearranged for each time step. The node which goes out of the calculation domain as time progresses was relocated at the intersection between the solid boundary and the line drawn between the node at previous and at current time steps. Results showed good agreement with data for a rectangular mold. To evaluate further the validity of the model, the area velocity of the resin-impregnated region during mold filling was calculated. The area velocity thus calculated was compared with the corresponding resin inlet velocity to check the mass conservation. A close agreement was observed, which renders confidence in the resin front proceeding algorithm. Numerical calculations were also performed for complicated geometries to illustrate the effectiveness of the current method.     

Gas transport in tight porous media: Gas kinetic approach

We describe the flow of gas in a porous medium in the kinetic regime, where the viscous flow structure is not formed in separate pores. Special attention is paid to the dense kinetic regime, where the interactions within the gas are as important as the interaction with the porous medium. The transport law for this regime is derived by means of the gas kinetic theory, in the framework of the model of “heavy gas in light one”. The computations of the gas kinetic theory are confirmed by the dimension analysis and a simplified derivation revealing the considerations behind the kinetic derivation. The role of the thermal gradient in the transport law is clarified.     

变系数各向异性热传导问题边界元解法

提出了一种用边界元法求解一般变系数各向异性热传导问题时建立基本解的方法,并导出了求解一般二维和三维各向异性稳态热传导问题的纯边界积分方程。所建立的基本解考虑了热导率是空间坐标的函数,因此所导出的积分方程可用于求解非均质材料传热问题。由热源项引起的域积分,运用径向积分法将其转换成边界积分,形成不需要内部点的纯边界元算法。给出了二维和三维问题3个分析算例,并通过将边界元法结果与有限元法结果进行对比,证明了方法的正确性和有效性。     

A full 3D finite element analysis of the powder injection molding filling process including slip phenomena

A full 3D finite element analysis system has been developed to simulate a Powder Injection Molding (PIM) filling process for general three‐dimensional parts. The most important features of the analysis system developed in this study are i) to incorporate the slip phenomena, the most notable rheological characteristics of PIM feedstock, into the finite element formulation based on a nonlinear penalty‐like parameter and ii) to simulate the transient flow during the filling process with a predetermined finite element mesh with the help of a volume fill factor and a melt front smoothing scheme. The treatment of the nonlinear slip boundary condition was successfully validated via a steady state pipe flow. For the purpose of comparisons, not only the numerical simulations but also experimental short‐shot experiments were performed with two 3D mold geometries using two typical materials of slip and no‐slip cases. The good agreements between the numerical and experimental results indicate that the melt front tracking scheme successfully simulates the transient filling process.     

3D finite element method for the simulation of the filling stage in injection molding

During the molding of industrial parts using injection molding, the molten polymer flow through converging and diverging sections as well as in areas presenting thickness and flow direction changes. A good understanding of the flow behavior and thermal history is important in order to optimize the part design and molding conditions. This is particularly true in the case of automotive and electronic applications where the coupled phenomena of fluid flow and heat transfer determine to a large extent the final properties of the part. This paper presents a 3D finite element model capable of predicting the velocity, pressure, and temperature fields, as well as the position of the flow fronts. The velocity and pressure fields are governed by the generalized Stokes equations. The fluid behavior is predicted through the Carreau Law and Arrhenius constitutive models. These equations are solved using a Galerkin formulation. A mixed formulation is used to satisfy the continuity equation. The tracking of the flow front is modeled by using a pseudo-concentration method and the model equations are solved using a Petrov-Galerkin formulation. The validity of the method has been tested through the analysis of the flow in simple geometries. Its practical relevance has been proven through the analysis of an industrial part.     

Analysis of coke under compressive loading: A combined approach using micro-computed tomography, finite element analysis, and empirical models of porous structures

The behaviour of coke, a brittle porous material, under compressive loads is a major factor in determining its quality. Coke samples were compressed using a test stage fitted inside a micro-computed tomography scanner. Three-dimensional images of the samples before and after compression were acquired. The ‘before’ images were used to create finite element (FE) models of the coke. The effective Young’s modulus was found by calibrating the linear elastic model using experimental data. The incremental displacement recorded during the experiments was then applied to the FE models. Comparison of FE analysis results with the ‘after’ images show high stress concentrations in the areas that cracked during the experiments, as well as reduced stresses in inerts. Displacement plots show a layered crushing pattern similar to that observed experimentally. Empirical models of brittle porous structures were used to estimate the elastic collapse stress of the coke wall. Results indicate that it may be the elastic collapse stress, rather than porosity, which best predicts whether a particular blend of coke will fail in compression.     

On the upscaling of reaction-transport processes in porous media with fast or finite kinetics

We show that for reaction-transport processes with fast kinetics (in the limit of thermodynamic equilibrium), conventional volume averaging for determining effective kinetic parameters applies only when the macroscopic variable approaches its equilibrium value. Even under such conditions, computing the effective mass transfer coefficient requires solving an eigenvalue problem, which couples the local microstructure with the global. Two examples, one involving a simple advection-dissolution problem and another a drying problem in a pore network, illustrate the theoretical predictions. Similar considerations apply for the case of finite kinetics, when the macroscale concentration approaches an equilibrium value. In that case, the effective kinetic parameter is not equal to the local, as typically assumed, but it becomes a function of the local Thiele modulus.     

Transport phenomena in porous media: A review

This paper, a review of the state of the art of the drying process in wet porous media, presents an overview of thermodynamic relations in heat treatment of synthetic fiber fabrics. Heat and mass transfer in wet porous media are coupled in a very complicated way. The structure of the solid matrix varies widely in shape. There is, in general, a distribution of void sizes, and the structures may be locally irregular. Energy transport in such a medium occurs by conduction in all of the phases. Mass transport occurs within voids of the medium. In an unsaturated state, these voids are partially filled with a liquid, whereas the rest of the voids contain some gas. It is a common misapprehension that nonhygroscopic fibers (i.e., those with intrinsically low moisture content) will automatically produce a hydrophobic fabric. The main significance of the fine geometry of a textile structure in contributing to resistance to water penetration can be stated in a different manner. Published in Russian in Teoreticheskie Osnovy Khimicheskoi Tekhnologii, 2006, Vol. 40, No. 1, pp. 17–30. This article was submitted by the author in English.