A methodology to reduce variability during vacuum infusion with optimized design of distribution media

Seemann Composites Resin Infusion Molding Process (SCRIMP) is a widely used version of Vacuum Assisted Resin Transfer Molding (VARTM) in which a highly permeable layer (distribution media) is placed on top of the dry preform to distribute the resin with very low flow resistance to reduce the filling and hence the manufacturing time. The flow patterns during filling may vary from part to part due to the variability associated with the material, part geometry, and layup of the assembly, which may result in race-tracking channels. The process is considered as reliable and robust only if the resin completely saturates the preform despite changing filling patterns caused by flow disturbances.The resin flow pattern can be manipulated with a tailored distribution media layout as it does impact the flow patterns significantly. The continuous distribution media layout over the entire part surface works well for very simple geometries with no to little potential for race-tracking along the edges. In this study we address complex cases, which require placement of an insert within the assembly, which will introduce race-tracking along its edges, and hence uniform placement of distribution media over the entire top surface will fail to yield a void free part. We introduce a methodology using a predictive tool to design an optimal shape of distribution media, which accounts for the flow variability introduced due to race-tracking along the edges of the inserts. This iterative approach quickly converges to provide the placement of distribution media on selective areas of the preform surface that ensures complete filling of the preform despite the variability. This approach has been validated with an experimental example and will help mitigate risk involved in manufacturing complex composites components with Liquid Molding.     

Flow analysis during compression of partially impregnated fiber preform under controlled force

Compression resin transfer molding (CRTM) is an alternative solution to conventional resin transfer molding processes. It offers the capability to produce net shape composites with fast cycle times making it conducive for high volume production. The resin flow during this process can be separated into three phases: (i) metered amount of resin injection into a partially closed mold containing dry fiber preform, (ii) closure of the mold until it is in contact with the fiber preform displacing all the resin into the preform and (iii) further mold closure to the desired thickness of the part compacting the preform and redistributing the resin. Understanding the flow behavior in every phase is imperative for predictive process modeling that guarantees full preform saturation within a given time and under specified force constraints.     

A new analytical method for particulate composites

A new semi-analytical approach to predict the mechanical behavior of heterogeneous (composite) media is presented. The eigenfunctions for the governing partial differential equation that the composite is subject to are derived in series form. The permissible functions that satisfy the continuity condition across the interface as well as the homogeneous boundary condition are obtained with the help of a computer algebra system. The Green’s function for the composite is then constructed from the eigenfunctions. Using the Green’s function, the physical/mechanical field in the composite is expressed. Numerical examples are shown.     

Simulation of coupling filtration and flow in a dual scale fibrous media

In this article, numerical simulation of suspension (particles filled-resin) flow through a fibrous media taking into account dual scale porosity in LCM (Liquid Composite Molding) processes is presented. During the flow, a strong interaction between the particle motion and the fluid flow takes place at the porous media wall (the fiber bundle surface). In this study, the Stokes–Darcy coupling is used to describe the resin flow at mesoscopic scale to treat the particles in suspension. A “fluid” model to describe the suspension flow, a “filtration” model to describe the particle capture and a “solid” model dedicated to the modeling of mass particles dynamics was used. The “solid” model is also operated to identify the particles retention.For validation, the numerical results of proposed model were compared with the experimental results from the literature and found in good agreement. Then, other numerical results studying the suspension’s rheological behavior are presented.     

Fundamentals of the double – decomposition concept for turbulent transport in permeable media

Environmental impact analyses as well as engineering equipment design can both benefit from reliable modeling of turbulent flow in porous media. A number of natural and engineering systems can be characterized by a permeable structure through which a working fluid permeates. Turbulence models proposed for such flows depend on the order of application of time and volume average operators. Two methodologies, following the two orders of integration, lead to different governing equations for the statistical quantities. This paper reviews recently published methodologies to mathematically characterize turbulent transport in porous media. A new concept, called double‐decomposition, is here discussed and models for turbulent transport in porous media are classified in terms of the order of application of the time and volume averaging operators, among other peculiarities. Within this paper Instantaneous Local Transport Equations are reviewed for clear flow before Time and Volume Averaging Procedures are applied to them. The Double‐Decomposition Concept is presented and thoroughly discussed prior the derivation of macroscopic governing equations. Equations for Turbulent Transport follow, showing detailed derivation for the mean and turbulent field quantities.     

Resistive heating of multidirectional and unidirectional dry carbon fibre preforms

The electrical conductivity (EC) of continuous carbon fibre (CF) layers is highly anisotropic and is expressed by a second order tensor. In the present work, using continuity equation for anisotropic media, the electrical conductivity of a dry CF multilayer preform can be predicted. Hence, the electrical conductivity tensor of the CF preform can be calculated for any stacking sequence. By means of the calculated electrical conductivity tensor of the multilayer preform, the elliptical form of the governing equation can be solved numerically. Based on this, the generated heat (Joule effect) can be determined. Introducing the generated heat into the heat transfer equation, the temperature field over the CF preform can be predicted. For the experimental verification, a thermal camera was used to record the temperature field developed on a CF multilayer preform under given electric potential field. The experimental results were compared to the respective numerical calculations of the temperature field, where the electrical conductivity tensor was calculated analytically based on the proposed methodology. In all the tested cases the calculated electrical conductivity tensor leads to a numerical model which is in excellent agreement with the experimental results.     

“Equivalent” permeability and flow in compliant porous media

Resin flow modeling for liquid composite molding processes is generally based on assumptions of rigid porous media. This is invalid for process variations utilizing compliant mold. Yet the models built on rigid porous media assumption are used with some success in analyzing such infusions.Previous work showed that for certain porous media the one dimensional flow patterns are similar to those in rigid porous media and the deformation effects can be included in a scaling factor for permeability.This note analyzes the one-dimensional linear and radial flows in porous media with generic constitutive relations between resin pressure, thickness and permeability. It shows that as long as the deformation remains moderate, the effect of deforming porous medium may be incorporated in a single scaling factor for material permeability. This scaling factor depends on material and applied injection pressure, but does not change with time, flow-front position or type of infusion (linear or radial).     

Multiscale modeling of unsaturated flow in dual-scale fiber preforms of liquid composite molding III: reactive flows

The woven, stitched or braided fabrics used in liquid composite molding (LCM) display partial saturation behind moving flow-front in an LCM mold which is caused by delayed impregnation of fiber tows. In this part 3 of the present series of three papers, a novel multiscale approach proposed in parts 1 and 2 [1] and [2] is adapted for modeling the unsaturated flow observed in the dual-scale fabrics of LCM under non-isothermal, reactive conditions. The volume-averaged species or resin cure equation, in conjunction with volume-averaged mass, momentum and energy (temperature) equations, is employed to model the reactive resin flow in the inter-tow (gap) and intra-tow (tow) regions with coupling expressed through several sink and source terms in the governing equations. A coarse global-mesh is used to solve the global (gap) flow over the entire domain, and a fine local mesh in form of the unit-cell of periodic fabrics is employed to solve the local (tow) flows. The multiscale algorithm based on the hierarchical computational grids is then extended to solve the dual-scale flow under reactive conditions. The simulation is compared with a two-color experiment and a previously published two-layer model. Significant differences between the temperatures and cures of the gap and tow regions of the dual-scale porous medium are observed. The ratio of pore volumes in the tow and gap regions, the effective thermal conductivity in the tows, and the reaction rate are identified as the important parameters for temperature and cure distributions in the gap and tow regions.     

Multiscale modeling of unsaturated flow of dual-scale fiber preform in liquid composite molding II: Non-isothermal flows

A novel multiscale approach is developed for modeling non-isothermal flows under unsaturated conditions in the dual-scale fabrics of liquid composite molding (LCM). The flow and temperature governing equations at the global or gap or inter-tow (∼m) level and the local or intra-tow (∼mm) levels are based on a previous dual-scale volume averaging method. To solve the coupled equations at two length-scales, a coarse global mesh is used to solve the global flow over the entire domain, and a fine local mesh in form of the unit-cell of periodic fabrics is employed to solve the local tow-impregnation process. (The latter is used to compute sink terms required for solving the former.) A multiscale algorithm based on the hierarchical computational grids is then proposed to solve the dual-scale flow under non-isothermal (but non-reactive) conditions. To test the proposed multiscale model, we first carry out a validation study in which the temperature histories predicted by the multiscale method are compared with experimental data available in a publication for a simple 1-D flow. Despite the lack of information about various model parameters, a reasonably good comparison with the experimental results is achieved. Then, the non-isothermal flow through a simple 1-D flow domain is carried out and the predictions of the multiscale simulation are compared with those of a previously published two-layer model. The multiscale predictions are found to be very similar to the two-layer predictions. A significant difference between the gap and tow temperatures is observed. The ratio of pore volumes in the tow and gap regions, thermal conductivity of the tows, and fiber types are identified as the important parameters for temperature distributions in the gap and tow regions. A further comparison with the single-scale flow simulation highlights significant differences between the conventional single-scale and the proposed dual-scale modeling approaches.     

Simulation of void formation in liquid composite molding processes

Air entrapment within and between fiber tows during preform permeation in liquid composite molding (LCM) processes leads to undesirable quality in the resulting composite material with defects such as discontinuous material properties, failure zones, and visual flaws. Essential to designing processing conditions for void-free filling is the development of an accurate prediction of local air entrapment locations as the resin permeates the preform. To this end, the study presents a numerical simulation of the infiltrating dual-scale resin flow through the actual architecture of plain weave fibrous preforms accounting for the capillary effects within the fiber bundles. The numerical simulations consider two-dimensional cross sections and full three-dimensional representations of the preform to investigate the relative size and location of entrapped voids for a wide range of flow, preform geometry, and resin material properties. Based on the studies, a generalized paradigm is presented for predicting the void content as a function of the Capillary and Reynolds numbers governing the materials and processing. Optimum conditions for minimizing air entrapment during processing are also presented and discussed.     

Cr(VI) adsorption on functionalized amorphous and mesoporous silica from aqueous and non-aqueous media

A mesoporous silica (SBA-15) and amorphous silica (SG) have been chemically modified with 2-mercaptopyridine using the homogeneous route. This synthetic route involved the reaction of 2-mercaptopyridine with 3-chloropropyltriethoxysilane prior to immobilization on the support. The resulting material has been characterized by powder X-ray diffraction, nitrogen gas sorption, FT-IR and MAS NMR spectroscopy, thermogravimetry and elemental analysis. The solid was employed as a Cr(VI) adsorbent from aqueous and non-aqueous solutions at room temperature. The effect of several variables (stirring time, pH, metal concentration and solvent polarity) has been studied using the batch technique. The results indicate that under the optimum conditions, the maximum adsorption value for Cr(VI) was 1.83 ± 0.03 mmol/g for MP-SBA-15, whereas the adsorption capacity of the MP-SG was 0.86 ± 0.02 mmol/g. On the basis of these results, it can be concluded that it is possible to modify chemically SBA-15 and SG with 2-mercaptopyridine and to use the resulting modified silicas as effective adsorbents for Cr(VI).     

Numerical analysis on pressure drop and heat transfer performance of mesh regenerators used in cryocoolers

An anisotropic porous media model for mesh regenerator used in pulse tube refrigerator (PTR) is established. Formulas for permeability and Forchheimer coefficient are derived which include the effects of regenerator configuration and geometric parameters, oscillating flow, operating frequency, cryogenic temperature. Then, the fluid flow and heat transfer performances of mesh regenerator are numerically investigated under different mesh geometric parameters and material properties. The results indicate that the cooling power of the PTR increases with the increases of specific heat capacity and density of the regenerator mesh material, and decreases with the increases of penetration depth and thermal conductivity ratio (a). The cooling power at a = 0.1 is 0.5-2.0 W higher than that at a = 1. Optimizing the filling scale of different mesh configurations (such as 75% #200 twill and 25% #250 twill) and adopting multi segments regenerator with stainless steel meshes at the cold end can enhance the regenerator’s efficiency and achieve better heat transfer performance.     

Analysis of Bénard convection in rectangular cavities filled with a porous medium

Summary Bénard convection in fluid-saturated porous cavities is studied in this research. The unsteady Navier-Stokes equations and energy equation describing the transient heat and fluid flow are expressed in primitive variables. A semi-implicit splitting finite element method is adopted to solve the coupled governing equations. The phenomena are discussed for a series of Rayleigh numbers, aspect ratios and different porous media. The results show that the strength of Bénard convection and heat-transfer rate become weaker due to the existence of more flow restriction in the porous media. Furthermore, the progress of flow evolution is also retarded compared with the non-porous medium. In some conditions, the heat transfer phenomenon is obviously altered because of the dramatic change in the flow pattern for different porous media.     

Coupled longitudinal-transverse behaviour of a geometrically imperfect microbeam

Based on the modified couple stress theory, the coupled longitudinal-transverse nonlinear behaviour of an imperfect microbeam is investigated numerically. The equations governing the longitudinal and transverse motions are obtained using Hamilton’s principle for the system with an initial geometric imperfection. The Galerkin scheme is employed to discretize the two partial differential equations of motion, yielding a set of second-order nonlinear ordinary differential equations with coupled terms. This set is cast into new set of first-order nonlinear ordinary differential equations and solved by means of the pseudo-arclength continuation technique. The nonlinear resonant response of the system along with bifurcations are presented via frequency–response curves. Moreover, the effect of different system parameter on the frequency–response curves is highlighted.     

An effective stress based numerical model for hydro-mechanical analysis in unsaturated porous media

 A fully coupled flow-deformation model is presented for the behaviour of unsaturated porous media. The governing equations are derived based on the equations of equilibrium, effective stress concept, Darcy's law, Henry's law, and the conservation of fluid mass. Macroscopic coupling between the flow and deformation fields is established through the effective stress parameters. The microscopic link between the volumetric deformations of the two pore system (i.e. the pore-air and the pore-water) is established using Betti's reciprocal theorem. Both links are essential for a proper modelling of flow and deformation in unsaturated porous media. The discretised form of the governing equations is obtained using the finite element technique. As application of the model, experimental results from several laboratory tests reported in the literature are modelled numerically. Good agreement is obtained between the numerical and the experimental results in all cases.     

弹性介质模糊有限元控制方程的快速解法

线弹性模糊有限元方法是分析弹性介质体模糊特性对结构响应产生不确定性影响的有效方法。即使对弹性介质体而言,模糊有限元控制方程的求解时间问题也是困扰其推广应用的主要障碍。为获得可靠可行的模糊有限元控制方程的快速求解方法,在深入研究弹性介质体的模糊源特点基础上,提出当引起结构模糊特性的力学参数为单源模糊数时,可以利用单源模糊数的运算特点来求解模糊有限元的控制方程,进而利用合成运算求解结构的模糊位移和模糊应力的分布。推导了基于单源模糊数运算的弹性介质模糊应力和模糊位移的计算表达式。应用模糊有限元求解的区间解法和快速解法对算例进行比较分析,结果表明了快速解法的正确性。     

Compressive response of Z-pinned woven glass fiber textile composite laminates: Modeling and computations

3D multi-layer and multi-representative unit cell (RUC) models are presented in order to capture the failure mechanisms of Z-pinned laminated textile composites presented in part 1 [Huang H, Waas A. Compressive response of Z-pinned woven glass fiber textile composite laminates: experiments, this issue] of this two part sequel. Simulations of 1, 9, 16, and 25-RUC models are compared to establish cell number effects in representing the textile composites for strength predictions. Further, simulations using multi-layer representations of the textile laminate are conducted to account for unintended stacking effects that occur during the manufacturing cycle. From the results of these simulations, the 3-layer model that has 16-RUCs in each layer is found to be the most adequate representation of the 3D multi-layer and multi-RUC models. Simulations show that stacking effects (layers not compacting and consolidating exactly as intended, resulting in a phase shift) during the manufacturing of the laminates, influence the outcome of the predicted compression strength.