基于VOF/PLIC界面追踪方法的RTM工艺充模过程数值模拟

针对基于Darcy定律的树脂传递模塑(RTM)工艺的充模过程数值模拟的局限性,将纤维预制体内的充填流动作为两相流(树脂相和空气相)处理,在动量方程中考虑了惯性项和粘性项,采用有限体积方法(FVM)离散控制方程,并与VOF/PLIC界面追踪方法相结合,发展了求解树脂在纤维预制体内非稳态流动问题的数值模拟方法.在此基础上开发了RTM工艺的充模过程数值模拟程序,其算例的数值模拟结果与解析解或实验结果吻合良好,验证了此数值模拟方法的有效性和可靠性.     

A finite element/nodal volume technique for flow simulation of injection pultrusion

In this paper, a finite element/nodal volume technique is developed to simulate the resin flow through the reinforcement during injection pultrusion processes. The governing equations for the pressure distribution and the conservation of resin mass during injection pultrusion are first derived. The solution algorithm and its numerical implementation are described. In particular, an algorithm is developed to advance the flow front by taking into account both the resin flow relative to the reinforcement and the movement of the pultruded part as a whole. The numerical technique developed is validated against a one-dimensional analytical solution derived. A number of numerical tests are then conducted to investigate the numerical performance and capability of the technique.     

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.     

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.     

Analysis of non-isothermal mold filling process in resin transfer molding (RTM) and structural reaction injection molding (SRIM)

In this paper, we present a modeling and numerical simulation of a mold filling process in resin transfer molding/structural reaction injection molding utilizing the homogenization method. Conventionally, most of the mold filling analyses have been based on a macroscopic flow model utilizing Darcy's law. While Darcy's law is successful in describing the averaged flow field within the mold cavity packed with a porous fiber preform, it requires experiments to obtain the permeability tensor and is limited to the case of porous fiber preform-it can not be used to model the resin flow through a double porous fiber preform. In the current approach, the actual flow field is considered, to which the homogenization method is applied to obtain the averaged flow model. The advantages of the current approach are: parameters such as the permeability and effective heat conductivity of the impregnanted fiber preform can be calculated; the actual flow field as well as averaged flow field can be obtained; and the resin flow through a double porous fiber preform can be modelled. In the presentation, we first derive the averaged flow model for the resin flow through a porous fiber preform and compare it with that of other methods. Next, we extend the result to the case of double porous fiber preform. An averaged flow model for the resin flow through a double porous fiber preform is derived, and a simulation program is developed which is capable of predicting the flow pattern and temperature distribution in the mold filling process. Finally, an example of a three dimensional part is provided.     

Resin infusion-based processes simulation : coupled Stokes-Darcy flows in orthotropic preforms undergoing finite strain

The aim of this paper is to present an overall model for the study of resin infusion based processes, in particular, the impregnation of a liquid resin through dry deformable fibrous reinforcements. This model can be appliedto a wide range of activities in many fields of engineering. Here, our approach based on a monolithic formulation in a level-set framework allows to strongly couple a Stokes-Darcy flow in low permeability media undergoing finite strains. The Stokes-Darcy coupled problem is solved using a mixed velocity-pressure formulation stabilized by a multi-scale method. A key feature of our approach is the fluid-solid interaction leading to couple a fluid/porous flow to a non-linear solid mechanics formulation. The interaction phenomenon due to the resin flow in the orthotropic highly compressible preform is based on both Terzaghi’s law and on explicit relation expressing permeability as function of porosity in finite strains mechanical framework. Finally, simulations of industrial design parts are performed to illustrate the abilities of our approach and the relevance of this fluid/porous-solid mechanics coupled problem for composite material process simulations.     

Curing simulation of thermoset composites

This paper deals with the modelling and simulation of resin flow, heat transfer and the curing of multilayer thermoset composite laminates during processing in an autoclave. Darcy's Law and Stokes’ slow-flow equations are used for the flow model and, for approximately isothermal flows, a similarity solution is developed. This permits the decoupling of the velocity and thermal fields. A two-dimensional convection–diffusion heat equation with an internal heat generation term is then solved numerically, together with the equation for the rate of cure, using a finite difference scheme on a moving grid. The simulations are performed with varying composite thicknesses, and a comparison of numerical results with known experimental data confirms the approximate validity of the model.     

用数值模型研究RTM工艺树脂流动规律

RIM成型过程中，树脂对纤维增强体的充分浸润是非常重要的一环。本文对树脂流动过程的特点进行了研究，建立了树脂流动控制方程。采用贴体坐标/有限差分法模拟了不同时刻树脂流动前沿曲线，计算结果与其他研究成果吻合良好。     

Numerical modelling of the boundary conditions on beams stuck transversely by a mass

In this paper, numerical results of a drop weight impact test examining the dynamic response of a clamped steel beams struck transversely at the centre by a mass with a rectangular indenter are presented. The numerical simulation showed that the results are very sensitive to the way in which the supports are modelled and thus this paper studies the modelling of the structural supports used to clamp the specimen beam in the experiment. The first approach simplifies the structural support as boundary condition on the nodes; the second model represents the entire support as the real approximation; the last approach uses simplified support plate model acting with the beam to simulate the experimental set up. The complete force-displacement curve is used to compare the plastic deformation of the impacted beams, thus the best approximation is selected for further calculations. The finite element model was performed using the LS-DYNA non-linear, dynamic finite element software. The numerical calculations can predict accurately the response of deflections, forces and absorbed energies, when proper boundary conditions are applied, in this case with shell elements representing the support plates.     

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.     

Finite element modeling of the filament winding process

A finite element model of the wet filament winding process was developed. In particular, a general purpose software for finite element analysis was used to calculate the fiber volume fraction under different process conditions. Several unique user defined subroutines were developed to modify the commercial code for this specific application, and the numerical result was compared with experimental data for validation. In order to predict the radial distribution of the fiber volume fraction within a wet wound cylinder, three unique user defined subroutines were incorporated into the commercial finite element code: a fiber consolidation/compaction model, a thermochemical model of the resin and a resin mixing model. The fiber consolidation model describes the influence of the external radial compaction pressure of a new layer as it is wound onto the surface of existing layers. The thermochemical model includes both the cure kinetics and viscosity of the resin. This model analyzes the composite properties and tracks the viscosity of the resin, which is a function of the degree of cure of the resin. The resin mixing model describes the mixing of “old” and “new” resin as plies are compacted. Validations were made by comparing image analysis data of fiber volume fraction in each ply for filament wound cylinders with the FEM results. The good agreement of these comparisons demonstrated that the FEM approach has can predict fiber volume fraction over a range of winding conditions. This approach, then, is an invaluable tool for predicting the effects of winding parameters on cylinder structural quality.     

复合材料层合板固化压实过程有限元数值模拟及影响因素分析

根据有效应力准则和达西定律建立了描述复合材料固化压实过程层合板压缩和树脂流动的二维有限元方程, 节点自由度为位移和树脂压力, 采用向后差分方法直接耦合积分求解以提高收敛速度。数值计算结果表明: 随着层合板厚度的增加, 厚度压缩率减小, 固化压实所需时间增加, 树脂在厚度方向的不均匀性逐渐增加。对于厚度较大的层合板, 采用提高固化压力和双面吸胶两种工艺对比情况说明, 后者可以显著提高压实程度并得到相对均匀的树脂含量分布。      

RTM工艺树脂流动过程数值模拟及实验比较

树脂充模是RTM工艺成型过程中的重要一环。研究了RTM工艺树脂流动过程的特点,建立了树脂渗流控制方程。采用贴体坐标/有限差分法模拟了树脂渗流过程,给出了不同时刻树脂流动前沿曲线及终止时刻压力场分布,计算结果与试验结果吻合良好。     

Simulation of groundwater flow in unconfined aquifer using meshfree point collocation method

For appropriate management of available groundwater, the flow behavior in the porous media has to be analyzed. The complex problem of groundwater flow can be studied by solving the governing equations analytically or by using numerical methods. As the analytical solutions are available only for simple idealized cases, numerical methods such as finite difference method (FDM) and finite element method (FEM) are generally used for field problems. Meshfree (MFree) method is an alternative numerical approach to solve complex groundwater problems in simple manner. MFree method eliminates the drawback of meshing and remeshing as in FDM and FEM which can translate to substantial cost and time savings in modeling. In this paper, a model using MFree point collocation method (PCM) with multi-quadric radial basis function (MQ-RBF) is proposed for 2D groundwater flow simulation. The accuracy of the developed model is verified with available analytical solution in literature. The developed model is applied initially for a hypothetical problem and further for a field problem to compute head distribution. The PCM model results for the hypothetical problem are compared with FEM simulations while that of field problem are compared with boundary element based model results. The PCM model results are found to be satisfactory showing the applicability of the present approach.     

Numerical simulation of injection/compression liquid composite molding. Part 1. Mesh generation

This paper presents a numerical simulation of injection/compression liquid composite molding, where the fiber preform is compressed to a desired degree after an initial charge of resin has been injected into the mold. Due to the possibility of an initial gap at the top of the preform and out-of-plane heterogeneity in the multi-layered fiber preform, a full three-dimensional (3D) flow simulation is essential. We propose an algorithm to generate a suitable 3D finite element mesh, starting from a two-dimensional shell mesh representing the geometry of the mold cavity. Since different layers of the preform have different compressibilities, and since properties such as permeability are a strong function of the degree of compression, a simultaneous prediction of preform compression along with the resin flow is necessary for accurate mold-filling simulation. The algorithm creates a coarser mechanical mesh to simulate compression of the preform, and a finer flow mesh to simulate the motion of the resin in the preform and gap. Lines connected to the top and bottom plates of the mold, called spines, are used as conduits for the nodes. A method to generate a surface parallel to a given surface, thereby maintaining the thickness of the intermediate space, is used to construct the layers of the preform in the mechanical mesh. The mechanical mesh is further subdivided along the spines to create the flow mesh. Examples of the three-dimensional meshes generated by the algorithm are presented.     

树脂传递模塑成型工艺中嵌套效应引起渗透率变异的实验与数值模拟

树脂传递模塑成型工艺(RTM)中最重要的变形模式之一是厚度方向压缩。厚度方向压缩减小了织物预成型体的厚度,使织物预成型体局部结构形式发生改变从而引起嵌套效应。嵌套效应不仅会减少织物预成型体的厚度,增加纤维的体积分数并改变孔隙率,而且相邻织物层嵌套效应具有一定的空间分散性,从而使得织物预成型体渗透率具有变异性。本文针对低黏度树脂设计了一种实验装置用以测量局部渗透率的空间分散性,随后建立了随机嵌套单胞模型,利用ANSYS/CFX有限元软件实现了单胞填充浸润的数值模拟,通过流量分析获得局部渗透率,并研究了渗透率的统计分布。通过实验结果与数值模拟结果相对比,验证数值模拟结果的可靠性。最后,基于渗透率的统计分布建立了随机渗透率场,并进行填充浸润的数值模拟,通过与传统恒定渗透率的方法进行比较,证明该方法具有更高的先进性。研究结果可以对未来RTM工艺的稳健性优化提供依据。      

Influence of the constitutive characteristics of resins on the composite materials delamination

This paper discusses the problem of interlaminar delamination in composite materials, with particular attention focused on the important role played by the resin properties. A Double Cantilever Beam (DCB) specimen has been modelled for finite element analysis assuming that the crack is situated inside a thin pure resin layer, similarly to the models proposed by Ozdil and Crews. A test program on the epoxy resin EPON 828, a typical resin commonly used for advanced composite systems for aerospace applications, has been carried out, in order to evaluate the mechanical properties; the results have shown a non-linear elastic behaviour without hysteresis effect. The non-linear relationship has been introduced in the bidimensional finite element model for the DCB specimen analysis. The stress and strain fields are used for the evaluation of the Energy Release Rate by means of a numerical model, based on an energetic approach such as the J-integral of Rice. The results show a considerable dependence on the constitutive relationship and give the opportunity of a more accurate evaluation of the toughness for experimental results from DCB specimen.     

Application of the level set method to the simulation of resin transfer molding

A new methodology is presented to simulate mold filling in resin transfer molding (RTM) using a combination of the level set and boundary element methods (BEMs). RTM is a composite manufacturing process where a liquid resin is injected in a closed rigid mold containing a dry fibrous reinforcement. Process simulation is motivated by the importance of tracking accurately the motion of the flow front during the mold filling stage. The BEM solves the equation governing the resin flow and the level set method is implemented to track the resin front in the mold. This formulation opens up new opportunities to improve RTM flow simulations and optimize injection molds. The present paper focuses on isothermal resin flow in undeformable porous medium. The implementation of the numerical algorithm is described and several examples of two-dimensional filling with single or multiple injection gates are presented. The robustness of the coupling and the ability to predict accurately the position of the front by this new model are discussed. It is also shown how dry spot formation can be tracked precisely during the simulation and how a generalization of this approach allows predicting resin flow across obstacles.     

大厚度复合材料曲面典型构件的工艺优化

大厚度复合材料的数值仿真存在缺乏实尺度验证、数值模型待优化等问题。本文针对真空辅助树脂传递模塑成型的大厚度复合材料曲面构件,通过大型风电叶片主梁的工艺仿真与实尺度实验验证,进行了工艺设计与工艺参数模型预测。首先对比研究了不同的工艺仿真方案;然后利用所选优化方案对树脂灌注方案进行工艺设计,并进行了实验验证;最后,提出了不同厚度制件的工艺参数预测模型。结果表明:所选优化方案可同时得到理想的计算效率和流动模拟结果;所设计工艺方案与实验吻合性良好;工艺参数预测模型所得结果与模拟结果基本一致。