气辅注射成型矩形腔中熔体流动的数值模拟

应用Hele-Shaw物理模型和改进的Ｃross流变模型对辅助射成型过程中充填区域内熔体的流动进行数值模拟,采用控制体积法对充模过程中的熔体前沿、熔体－气体边界进行跟踪,运用有限元／有限差分混合数值方法求解气体注射阶段的速度场、压力场、温度场,以图表的形式列举了不同时刻压力场的分布和充模过程中的流线图。在计算过程中,采用压力场和温度场耦合的方法。     

基于SPH方法的微注射成型数值模拟

基于无网格方法和黏性本构方程,开展微注射成型数值模拟的研究。采用光滑粒子流体动力学的粒子近似法离散N-S 控制方程组,求解速度场、压力场、温度场等物理场的变化规律。以应用于生物医学领域带有细微针头的聚合物微针为例,进行充型过程的数值模拟,模拟结果与实验结果基本一致。     

基于P1/PO四面体宏元的三维注塑充填速度场压力场有限元数值模拟

计算效率和解的稳定性是影响三维注塑充填有限元数值模拟的关键因素.针对黏性不可压缩聚合物熔体三维充填过程的速度场和压力场,以提高计算机求解速度为出发点,分析了采用P1/P0四面体单元(速度线性,压力常数)得到的有限元方程的解不收敛的原因,提出一种采用P1/P0四面体宏元离散空间域的求解方案,从而降低了求解的自由度数量,提高了计算速度.通过模拟"圆管中定黏度流体的稳态流动"考察了该求解方案的模拟精度,通过模拟"圆管中定黏度流体的瞬态充填"比较了采用P1/P0四面体宏元和P2/P1四面体单元(二次速度,线性压力)的计算时间.最终将该方案应用到三维注塑充填的数值模拟中.     

基于P1/PO四面体宏元的三维注塑充填速度场压力场有限元数值模拟

计算效率和解的稳定性是影响三维注塑充填有限元数值模拟的关键因素.针对黏性不可压缩聚合物熔体三维充填过程的速度场和压力场,以提高计算机求解速度为出发点,分析了采用P1/P0四面体单元(速度线性,压力常数)得到的有限元方程的解不收敛的原因,提出一种采用P1/P0四面体宏元离散空间域的求解方案,从而降低了求解的自由度数量,提...     

数值模拟技术在橡胶冷流道设计中的应用研究

将数值模拟技术与正交试验方法相结合,对橡胶注射模具冷流道浇注系统的温度场进行了数值分析及研究。数值计算采用隐式定常求解,用k-ε湍流模型封闭运动方程,近壁区的流动采用标准的壁面函数法,固体壁面用无滑移边界条件,压力—速度耦合用SIMPLE算法。试验设计采用三水平三因素的正交试验法,得出三个不同水平的导热油油路直径、导热油的入口温度以及入口速度温度场分布,经过统计计算获得最佳结果：导热油油路直径为10mm、导热油的入口温度为95℃、流动速率为3.5m/s。     

注塑充模流动过程灵敏度数值分析

从注塑模充模过程控制方程出发,建立了注塑成型充模过程物理场对设计参数瞬态连续灵敏度分析理论,得到了充模过程压力场、温度场、速度场等物理场对设计参数的灵敏度控制方程.数值分析沿用了注塑模流动分析的基本思想,压力灵敏度采用有限元法、通过对时间和厚度方向的差分求解温度灵敏度,借助于控制体积的概念得到运动边界灵敏度分析.数值算例分析了注射压力对注射流率、熔体温度的设计灵敏度,与数值实验吻合良好.     

数值模拟方法在橡胶冷流道设计中的应用研究

将数值模拟方法与正交试验方法相结合,对橡胶注射模具冷流道浇注系统的温度场进行数值分析和研究。数值计算采用隐式定常求解,用k-ε湍流模型封闭运动方程,近壁区的流动采用标准的壁面函数法,固体壁面用无滑移边界条件,压力-速度耦合用SIMPLE算法。试验设计采用三水平三因子的正交试验法,得出不同水平组合下的温度场分布,导热油油路直径为10 mm、导热油入口温度为95℃、导热油入口流速为3.5 m·s-1时,胶料温度最佳,温度分布均匀。     

气体辅助注射成型充填过程的数值模拟

描述了气体辅助注射成型的工艺过程及熔体充填和气体穿入的数学模型,采用有限元/有限差分/控制体积法计算充填阶段的压力场和温度场,确定熔体前沿和熔体/气体界面两类移动边界,并对典型制件充模过程进行了模拟.     

带有矩形嵌件薄壁型腔内熔接过程动态模拟

为了准确模拟具有对称结构的带有矩形嵌件的薄壁型腔内熔接线的动态形成过程,采用Level Set/Ghost方法追踪充填阶段聚合物熔体前沿界面。引入具有高阶精度且数值稳定无振荡的5WENO（the fifth order weighted essentially nonoscillatory）格式对Level Set/Ghost方程进行数值求解,耦合求解物理量控制方程的一般差分格式实现熔接过程的动态模拟。数值算例对整个流场的压力、温度及速度进行了分析和讨论,并将熔接区域的压力、温度和非熔接区域的压力、温度进行了比较。数值结果与理论分析结果一致,且与前人数值结果相比有很好的精度。     

用Galerkin方法模拟黏性可压缩流体的充模过程

建立了黏性可压缩流体的控制方程，给出了适合注射成型特点的边界条件及黏度模型，导出了求解压力场的控制方程。用Galerkin方法建立了有限元求解的变分方程和代数方程，给出了迭代求解步骤；采用隐式格式及“上风”法离散能量方程、求解温度场，开发了模拟程序。     

求解多维半透明介质内辐射传递的谱元法

直角坐标系下的辐射传递方程可以看作一类特殊的对流扩散方程,且具有强对流特性。采用数值方法求解该问题需要特别的稳定技术,否则计算结果往往会出现非物理振荡现象。本文发展了基于流向迎风彼得罗夫-伽辽金（SUPG）格式的谱元法来求解多维半透明介质内的辐射传递。采用3个算例对SUPG谱元法求解多维半透明介质内辐射传递的性能进行了检验。结果表明,与伽辽金谱元法相比,SUPG谱元法有效地消除了解的非物理振荡现象,同时与解析解及文献中的结果相比较,SUPG谱元法对于求解多维半透明介质内的辐射传递有着很好的精度。     

A model of advancing flow front in RIM

A two-dimensional model is developed for mold filling in Reaction Injection Molding using a Petrov-Galerkin finite-element method with free surface parameterization. Dependence of viscosity on the conversion and temperature is represented by the Castro-Macosko function. The model predicts the velocity, pressure, temperature, and conversion distributions with time during the filling stage of a rectangular mold. No a priori assumptions are made regarding the shape of the advancing flow front, or regarding any variables in the flow front region. The accuracy is further improved by using the Petrov-Galerkin formulation, rather than the Galerkin formulation. The results are presented for well-characterized polyurethane systems, for which reliable experimental data is available. The predictions of the model for the pressure rise are in excellent agreement with the experimental data (1) even close to the gel point. These refined predictions are expected to assist in estimating fiber orientation and bubble growth in the final RIM parts, in which the flow front region plays the most important role. Characterization of polyurethane/polyurea and polyurea materials is underway, and will be subsequently incorporated in the model.     

ELEMENT METHOD TO NONLINEAR TRANSIENT DIFFUSION-CONVECTION-REACTION SYSTEM

Streamline upwind Petrov-Galerkin finite element method (SUPG FEM) was considered to solve for the general chemically reactive flow system with convection, diffusion, and reaction. A nonlinear transient pseudo-homogeneous catalytic reactor model with Dankwert boundary conditions in two-dimensional domain was selected as an numerical example. The effect of velocity distribution on the dynamics of the system and the wrong way behavior was discussed in detail and the dependence of the steady-state solution upon a set of dimensionless parameters was investigated. In addition, for the numerical test of the discontinuity capturing scheme, the one-dimensional pseudo-homogeneous plug flow reactor model which incudes a discontinuity by a high convection and reaction rale was considered and the SUPG FEM was applied to solve for the mode) equation. The results from the SUPGFEM were then compared with the theoretical result from the method of characteristics and also with those from various formula based on the streamline upwind biased finite difference method (SUB FDM). Both the SUPG FEM and the SUB FDM were found to be the effective numerical techniques for capturing the discontinuity of the convective flow system and reducing the numerical oscillations.     

Multi-scale finite element modelling using bubble function method for a convection-diffusion problem

Due to the multi-scale nature of the convection-diffusion equation the standard Galerkin method fails to predict accurate and stable results. A multi-scale finite element method based on the bubble function approach has been developed and applied to this problem. Finite element formulations based on the discontinuous weighting functions including the streamline upwind Petrov-Galerkin (SUPG) method are also evaluated. The results show that the multi-scale method provides stable and accurate results and matches very well the analytical solution.     

Modeling of injected pultrusion processes: A numerical approach

Injected pultrusion (IP) is an attractive process for high volume, high performance, and low cost manufacture of continuous fiber reinforced polymer matrix composites. In this work we focus our attention on development of a computer simulation model for the IP process. First, the governing equations for conservation of mass, momentum, and energy are developed using a local volume averaging approach. In turn, a computer simulation model of the IP process is developed using finite element/control volume (FE/CV) and finite difference techniques. Specifically, the equation of continuity and conservation of momentum are solved in 2-D using a Galerkin FE/CV technique. The energy and chemical species balance equations are solved in 3-D, where streamline upwind Petrov-Galerkin (SUPG) or streamline upwind (SU) FE/CV are used to discretize the equations in two dimensions while finite differences have been used in the third dimension. The chemical species balance equation is solved in the Lagrangian frame of reference using finite differences. Different numerical formulations (Galerkin, Lagrangian, SU, and SUPG) are used to solve a number of benchmark problems to determine the best numerical formulation. It is shown that for coarse discretization, Streamline Upwind methods perform consistently better than the other methods. However, for refined meshes, the Lagrangian method produces the best solution for a given CPU time. Also, using the simulation model, the effect of fiber pull speed, reinforcement anistropy, and taper of the die on the quality of the product is studied. It is shown that the simulation model can be effectively used to design the die geometry as well as to optimize the operating conditions for a given product.     

Non-isothermal flow of a polymeric liquid through rounded rectangular ducts

The 3D non-isothermal creeping flow of nylon-6 in a bent rectangular duct is studied numerically. A differential-type non-isothermal White-Metzner constitutive equation is used for this flow simulation. Computational results are obtained by the elastic-viscous split-stress (EVSS) finite element method, incorporating the streamline-upwind Petrov-Galerkin (SUPG) scheme. The generated thermal field is entirely due to viscous heating. Essential flow characteristics, including temperature distribution in the flow field, are predicted. The resulting average Nusselt numbers along the walls and dimensionless bulk temperatures along the channel are obtained. Subsequently, the effects of flow-rate and geometry are investigated. Polym. Compos. 25:375–383, 2004. © 2004 Society of Plastics Engineers.     

带筋注塑制品截面充填过程数值模拟

采用有限元法,模拟计算了带加强筋的注塑制品截面充填过程的流场。通过设计两个算例,模拟得到带加强筋的注塑制品截面充填过程中其厚度方向上的速度场、压力场、熔体前沿以及速度和压力的变化历史。由速度场的变化历史特别是剪切历史可以得到流动诱导的纤维取向分布。     

Simulation of injection–compression‐molding process. II. Influence of process characteristics on part shrinkage

A numerical algorithm is developed to simulate the injection–compression molding (ICM) process. A Hele–Shaw fluid‐flow model combined with a modified control‐volume/finite‐element method is implemented to predict the melt‐front advancement and the distributions of pressure, temperature, and flow velocity dynamically during the injection melt filling, compression melt filling, and postfilling stages of the entire process. Part volumetric shrinkage was then investigated by tracing the thermal–mechanical history of the polymer melt via a path display in the pressure–volume–temperature (PVT) diagram during the entire process. Influence of the process parameters including compression speed, switch time from injection to compression, compression stroke, and part thickness on part shrinkage were understood through simulations of a disk part. The simulated results were also compared with those required by conventional injection molding (CIM). It was found that ICM not only shows a significant effect on reducing part shrinkage but also provides much more uniform shrinkage within the whole part as compared with CIM. Although using a higher switch time, lower compression speed, and higher compression stroke may result in a lower molding pressure, however, they do not show an apparent effect on part shrinkage once the compression pressure is the same in the compression‐holding stage. However, using a lower switch time, higher compression speed, and lower compression stroke under the same compression pressure in the postfilling stage will result in an improvement in shrinkage reduction due to the melt‐temperature effect introduced in the end of the filling stage. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 75: 1640–1654, 2000     

三维非等温非牛顿流体充模过程的建模与模拟

为了避免使用速度延拓法处理自由表面边界条件,更真实地反映非牛顿熔体的充模过程,耦合Navier-Stokes方程组,建立了三维实体气液两相流模型。采用基于SIMPLE算法的同位网格有限体积法求解流场物理量,并结合Level Set界面追踪技术实现了非等温熔体充模阶段的动态模拟。为防止出现三维情形下棋盘型压力场,利用同位网格动量插值技术,解决压力与速度失耦的问题。分析了充模过程中,流场物理量的变化情况,研究了注射速率、入口温度等对充模过程及熔体凝固层厚度的影响,得出了与实验相吻合的模拟结果。数值结果表明,三维实体气液两相流模型能更准确地描述聚合物熔体的充模过程;当注射速率较大、入口温度较高时,充模时间较短,熔体凝固层的厚度较小。