An efficient solver of the saturation equation in liquid composite molding processes

A major issue in Liquid Composite Molding Process (LCM) concerns the reduction of voids formed during the resin filling process. Reducing the void content increases the quality of the composite and improves its mechanical properties. Most of modeling efforts on process simulation of mold filling has been focused on the single phase Darcy’s law, with resin as the only phase, ignoring the formation and transport of voids. The resin flow in a partially saturated region can be characterized as two phase flow through a porous medium. The mathematical formulation of saturation in LCM takes into account the interaction between resin and air as it occurs in a two phase flow. This model leads to the introduction of relative permeabilities as a function of saturation. The modified saturation equation is obtained as a result, which is a non-linear advection-diffusion equation with viscous and capillary phenomena. In this work, a flux limiter technique has been used to solve a modified saturation equation for the LCM process. The implemented algorithm allows a numerical optimization of the injected flow rate which minimizes the micro/macroscopic void formation during mold filling. Some preliminary numerical results are presented here in order to validate the proposed mathematical model and the numerical scheme. This formulation opens up new opportunities to improve LCM flow simulations and optimize injection molds.     

A two-phase flow model to simulate mold filling and saturation in Resin Transfer Molding

This paper addresses the numerical simulation of void formation and transport during mold filling in Resin Transfer Molding (RTM). The saturation equation, based on a two-phase flow model resin/air, is coupled with Darcy’s law and mass conservation to simulate the unsaturated filling flow that takes place in a RTM mold when resin is injected through the fiber bed. These equations lead to a system composed of an advection–diffusion equation for saturation including capillary effects and an elliptic equation for pressure taking into account the effect of air residual saturation. The model introduces the relative permeability as a function of resin saturation. When capillary effects are omitted, the hyperbolic nature of the saturation equation and its strong coupling with Darcy equation through relative permeability represent a challenging numerical issue. The combination of the constitutive physical laws relating permeability to saturation with the coupled system of the pressure and saturation equations allows predicting the saturation profiles. The model was validated by comparison with experimental data obtained for a fiberglass reinforcement injected in a RTM mold at constant flow rate. The saturation measured as a function of time during the resin impregnation of the fiber bed compared very well with numerical predictions.     

Experimental validation of post-filling flow in vacuum assisted resin transfer molding processes

In Liquid Composite Molding (LCM) processes with compliant tool, such as Vacuum Assisted Resin Transfer Molding Process (VARTM), resin flow continues even after the inlet is closed due to the preform deformation and pressure gradient developed during infusion. The resin flow and thickness changes continue until the resin pressure becomes uniform or the resin gels. This post-filling behavior is important as it will determine the final thickness and fiber volume fraction distribution in the cured composite. In this paper, a previously proposed one dimensional coupled flow and deformation process model has been compared with the experimental data in which the resin pressure and part thickness at various locations during the post-filling stage is recorded. Two different post-infusion scenarios are examined in order to determine their impact on the final part fiber volume fraction and thickness. The effects of different venting arrangements are demonstrated. The model predictions compare favorably with the experimental data, with the minor discrepancies arising due to the variability of material properties.     

Resin flow modeling in compliant porous media: an efficient approach for liquid composite molding

In Liquid Composite Molding (LCM) processes such as Resin Transfer Molding (RTM) and Vacuum Assisted Resin Transfer Molding (VARTM), complete saturation of reinforcement with resin during the injection step is necessary. In RTM, reinforcement experiences no deformation during infusion but for other methods reinforcement thickness changes during the injection. To model resin flow in compliant media, RTM flow simulation software is routinely used. It has been successful in predicting flow patterns if appropriate “effective” permeability is used. The proper approach requires new implementation that couples the deformation and pressure field which is computationally more demanding. Our work describes a computationally efficient methodology to add corrections into RTM simulation environment to account for deformation. This approach is verified with known solutions and experimental validation. The simulation is applied to a complex geometry which demonstrates better computational performance and confirms that the “effective” permeability may be used to model flow in complex geometries.     

Dynamic saturation curve measurement in liquid composite molding by heat transfer analysis

In Liquid Composite Molding (LCM) processes the saturation of the reinforcement by the resin may induce the creation of porosity in the preform affecting the final properties of the composite. The purpose of this work concerns the development of an experimental protocol and the associated modeling to identify the dynamic saturation curve during filling by taking advantage of sharp contrasts of thermal properties existing between dry and fully-saturated reinforcement. To identify saturation, several injections were performed with a laboratory RTM mold for which thermal design allows accurate control of heat transfer. Several heat flux sensors were used to identify the saturation curve. Sensitivity analysis proves the feasibility of the method. The results are compared with a conductometric method with good agreement. Evolution of residual voids identified for several flow rates are also consistent with those expected according to the capillary number.     

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.     

LCM工艺实时监测技术的影响因素

为了提高复合材料液体成型(LCM) 工艺构件的质量稳定性和降低成本, 建立了直流电实时监测系统。实验表明, 该监测系统能够准确地反映监测点处树脂流动前锋的到达及其固化过程。研究了主要工艺因素对监测信号的影响规律, 发现系统对不同的树脂体系的响应差别较大, 监测饱满值随工艺温度的升高而增大, 随监测铜丝裸露长度的增加而增大, 纤维体积含量和纤维铺放角度对监测信号的影响不大。      

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.     

A methodology for flow-front estimation in LCM processes based on pressure sensors

Liquid Composite Molding (LCM) processes offer nowadays considerable advantages for composite manufacturers; nevertheless, their robustness is still an open issue, since part quality is sensitive to slight material and process variations, mainly arising during preform impregnation. An accurate monitoring system is thus required for early identification of filling troubles and potentially adoption of control actions. This work proposes an approach for resin flow monitoring, based on a combination of a sensing system and numerical modeling, which can be easily implemented into a generic LCM process. Using pressure data provided by few sensors placed in strategic positions inside the mold cavity, the developed methodology enables reconstruction of flow-front patterns at any impregnation time, without simulation of cavity filling. The effectiveness of the methodology is demonstrated by two test cases, which validate the approach through comparison between real and estimated flow-front profiles. Potential and limitations of the method in presence of flow disturbances have been studied through several virtual experiments, defining the range of applicability and key issues for future development.     

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.     

Three-dimensional reconstruction of resin flow using capacitance sensor data assimilation during a liquid composite molding process: A numerical study

Liquid composite molding (LCM) is a method to manufacture fiber-reinforced composites, where dry fabric reinforcement is impregnated with a resin in a molding apparatus. However, the inherent process variability changes resin flow patterns during mold filling, which in turn may cause void formation. We propose a method to reconstruct three-dimensional resin flow in LCM, without embedding sensors into the composite structure. Capacitance measured from pairs of electrodes on molding tools and the stochastic simulation of resin flow during an LCM process are integrated by a sequential data assimilation method based on the ensemble Kalman filter; then, three-dimensional resin flow and permeability distribution are estimated simultaneously. The applicability of this method is investigated by numerical experiments, characterized by different spatial distributions of permeability. We confirmed that changes in resin flow caused by spatial permeability variations could be captured and the spatial distribution of permeability could be estimated by the proposed method.     

Simulation of the three-dimensional non-isothermal mold filling process in resin transfer molding

Numerical simulation of resin transfer molding (RTM) is known as a useful method to analyze the process before the mold is actually built. In thick parts, the resin flow is no longer two-dimensional and must be simulated in a fully three-dimensional space. This article presents numerical simulations of three-dimensional non-isothermal mold filling of the RTM process. The control volume/finite element method (CV/FEM) is used in this study. Numerical formulation for resin flow is based on the concept of nodal partial saturation at the flow front. This approach permits to include a transient term in the working equation, removing the need for calculation of time step to track the flow front in conventional scheme. In order to compare the results of the nodal partial saturation concept with the conventional method, a numerical scheme based on the quasi-steady state formulation is also presented. The computer codes developed based on both numerical formulations, allow the prediction of flow front positions; and pressure, temperature and conversion distributions in three-dimensional molds with complicated geometries. The validity of the two schemes is evaluated by comparison with analytical solutions of simple geometries. In all instances excellent agreement is observed. Numerical case studies are provided to demonstrate the effectiveness of the developed computer codes. The results show that the numerical procedure based on the nodal partial saturation concept, developed in this study, provides numerically valid and reasonably accurate predictions.     

A flux limiter strategy for solving the saturation equation in RTM process simulation

The main aim of this work is the proposal of a numerical procedure for solving the saturation equation in RTM process simulation. In order to analyze in more detail the progressive impregnation of a fibrous preform by a fluid resin, the numerical model here proposed considers the flow through a partially saturated medium, including the dependence of permeability on the saturation degree. The model consists of an elliptic equation governing the pressure distribution and a transport hyperbolic equation governing the evolution of the saturation. A global flux limiter fixed mesh strategy is proposed for solving the transport equation with source term which describes the saturation evolution in RTM process. The flux limiter method has the ability to limit the extra numerical diffusion introduced by standard first-order schemes. This formulation could be an appealing choice for improving RTM flow simulations and optimize injection processes. Some preliminary numerical results are presented in order to validate the proposed numerical strategy.     

Numerical prediction and experimental characterisation of meso-scale-voids in liquid composite moulding

Pressure gradients that drive the resin flow during liquid composite moulding (LCM) processes can be very low while manufacturing large composite parts. Capillary pressure becomes the predominant force for tow impregnation and thus meso-scale-voids can be generated, reducing the part quality. In contrast, micro-voids are created at high resin pressure gradients. In this work, a numerical method is presented to predict the creation of meso-scale-voids and their evolution. Experimental validation is conducted by measuring void content of produced composite parts with micro-computed tomography (μ-CT). Additionally, the void content as a function of the modified capillary number Ca^* is determined and the influence of the fibre volume content in the bundles on the meso-scale- and micro-void content is studied.     

Dynamic saturation curve measurement for resin flow in glass fibre reinforcement

A methodology is presented to determine the saturation curve of a resin/glass fabric system, during infiltration in a transparent mould under constant flow rate. Video acquisitions are transformed by image analysis into saturation level versus position and time, and coupled to inlet pressure measurements. A numerical multiphase flow model is then used to simulate the infiltration for various combinations of drainage curve parameters. The numerical parameters to describe the saturation and relative permeability are determined by response surface optimization. The drainage curve and relative permeability equations determined at one time are shown to adequately describe the entire injection process, and to be flow-rate dependent.     

Coupling filtration and flow during liquid composite molding: Experimental investigation and simulation

Molding composites constituted of fiber reinforcements, resin and fillers is of prime interest for many transportation applications. Dealing with the flow of particle-filled resin in a fibrous network raises the issue of particle retention and viscosity increase. The present study aims at simulating such molding through an efficient coupling between a filtration model, that has been previously described, and a flow model (Darcy’s law). First, filling experiments are realized so as to separate cases: cake filtration, retention and no retention for two types of single-scale porous materials (polyester felt and glass fiber mat) injected with a resin filled with micro-beads. Then results of filler content, viscosity, permeability, pressure, retention profiles are simulated from the coupling between filtration and flow. Experimental data of filler profiles in the final parts, resin flow front evolution and injection times are compared with predictions obtained from the simulation.     

Modeling the impact of capillary pressure and air entrapment on fiber tow saturation during resin infusion in LCM

Traditionally, capillary effects have been neglected when modeling the filling stage of Liquid Composite Molding processes. This simplification is justified because the inlet resin pressures are much higher than the capillary pressure. This simplification is also acceptable when impregnating fabrics in which their fiber tows saturate at the same rate as the bulk preform. However, this assumption is questionable for fabrics that exhibit dual scale in which the fiber tows saturate at a much slower rate than the bulk preform. In such cases, the capillary pressure can influence the time to saturate a fiber tow significantly and impact the overall impregnation dynamics. Since the flow front velocity inside the fiber tows is significantly smaller than the flow around them, it is important to include the capillary pressure that may aid the saturation of the tow. In this paper, we modify our existing simulation that can predict the filling of the bulk preform and the saturation of the fiber tows to include the capillary forces at the fiber tow level. Important parameters are identified and grouped in non-dimensional form. A parametric study is conducted to examine the role of these dimensionless parameters on the overall tow saturation levels. The modeling is extended to include the effect of entrapped air inside the tows on the overall saturation of the preform. An experimental technique using the optical properties of vinyl ester and glass fiber was used to qualitatively validate the proposed model.     

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。     

Mathematical Analysis of Resin Flow through Fibrous Porous Media

Resin flow through fiber preforms was analyzed mathematically. Closed form solutions for fiber volume fraction distribution and pressure field during resin infusion into fiber preforms were suggested, and a new effective permeability was defined. The effect of preform compressibility on the fiber volume fraction and pressure distributions in resin-saturated region was investigated analytically. The findings show that the compaction behavior of preforms has significant impact on the resin infusion process. The solutions derived analytically in this study can provide insight into a liquid composites molding (LCM) process.     

液体模塑成型工艺二维径向非饱和流动数值模拟

通过引入沉浸函数建立了双尺度多孔介质非饱和流动模型,并采用有限元/控制体积法实现了恒压及恒流注射条件下液体模塑成型（LCM）工艺二维径向非饱和流动的数值模拟,得到了不同注射条件下纤维织物内的压力场分布及半饱和区域长度随时间的变化规律,并将双尺度非饱和理论结果与单尺度饱和理论结果进行对比。结果表明：非饱和流动过程中,半饱和区域内的压力和压力梯度明显下降;半饱和区域长度随时间逐渐增加随后保持稳定,当流动前沿到达出口后半饱和区域长度开始逐渐减小;当两个主方向渗透率不同时,沿主方向半饱和区域长度也不同,渗透率越大该方向的半饱和区域长度也越大,纤维织物完全浸润时间取决于较小的渗透率。研究结果对合理预测树脂填充过程中压力分布及纤维预制件的浸润具有指导意义。