Nonisothermal transient filling simulation of fiber suspended viscoelastic liquid in a center‐gated disk

The present study numerically investigates a fiber orientation in injection‐molded short fiber reinforced thermoplastic composite by using a rheological model, which includes the nonlinear viscoelasticity of polymer and the anisotropic effect of fiber in the total stress. A nonisothermal transient‐filling process for a center‐gated disk geometry is analyzed by a finite element method using a discrete‐elastic‐viscous split stress formulation with a matrix logarithm for the viscoelastic fluid flow and a streamline upwind Petrov–Galerkin method for convection‐dominated problems. The numerical analysis result is compared to the experimental data available in the literature in terms of the fiber orientation in center‐gated disk. The effects of the fiber coupling and the slow‐orientation kinetics of the fiber are discussed. Also, the effect of the injection‐molding processing condition is discussed by varying the filling time and the mold temperature. POLYM. COMPOS., 2011. © 2010 Society of Plastics Engineers     

Application and evaluation of the method of ellipses for measuring the orientation of long,semi‐flexible fibers

The method of ellipses (MoE) is a common experimental technique utilized to quantitatively determine the orientation state of a population of rigid fibers within a fiber–polymer composite. In this research, the validity of applying the MoE to long, semi‐flexible fiber systems in which the majority of fibers are flexible is discussed. The components of the orientation tensor were first determined for a composite formed by a homogenous, simple shear field. The minimum acceptable image analysis width, or bin width, for the selected geometry was found to be ∼5.5 mm, or 1.4 times the average fiber length. This modified bin width was then used to determine the orientation at multiple percentages of flow within an injection‐molded, center‐gated disc, and compared to orientation values obtained utilizing the traditional, 0.7‐mm bin width. The results show that the traditional, 0.7‐mm bin width is sufficient for analysis of the center‐gated geometry. This fortuitous result is attributed to the axisymmetric nature of the center‐gated geometry, and the highly transverse fiber alignment seen within the samples, especially at moderate to high percentages of flow. In more complex flows, it is expected that the conventional bin width will not apply. POLYM. COMPOS., 2013. © 2013 Society of Plastics Engineers     

Prediction of fiber orientation in the injection molding of long fiber suspensions

The properties of long glass fiber reinforced parts are highly dependent on the fiber orientation generated during processing. In this research, the orientation of concentrated long glass fibers generated during the filling stage of a center‐gated disk (CGD) mold was simulated. The orientation of the fibers was calculated using both the Folgar‐Tucker model and a recently developed semiflexible Bead‐Rod model. Rheologically consistent model parameters were used in these simulations, as determined from a previously proposed method, using a sliding plate rheometer and newly modified stress theory. The predicted CGD orientations were compared with experimentally measured values obtained from the parts. Both models performed very well when using model parameters consistent with the independent rheological study, and the results provide encouragement for the proposed method. Comparatively, the Folgar‐Tucker model provided slightly better orientation predictions up to 20% of the fill radius, but above 20% the Bead‐Rod model predicted better values of the orientation in both the radial and circumferential directions. The Folgar‐Tucker model, however, provided better orientation values perpendicular to the flow direction. Lastly, both models only qualitatively represented the orientation above 70% of the fill radius where frontal flow effects were suspected to be non‐negligible. The uniqueness of this research rests on a method for obtaining model parameters needed to predict fiber orientation which are independent of the experiments being simulated and a method for handling long semiflexible fiber suspensions. POLYM. COMPOS., 2012. © 2012 Society of Plastics Engineers     

Multi-scale mathematic modeling of non-isothermal polymeric flow of fiber suspensions

Multi-scale numerical analysis of non-isothermal polymeric flow of fiber suspensions is presented by numerical simulation using a multi-scale modeling. And the multi-scale modeling is established by the coupling of three scales, the macroscopic flow field, the mesoscopic fiber orientation and the microscopic macromolecular information. The constitutive equation which incorporates specific features of polymeric melt of fiber suspensions and its constituents is represented by linear sum of the stress contributions from the three scales. Using the multi-scale modeling, numerical simulations of the polymeric flow of fiber suspensions through a planar contraction cavity and the predicted stress distribution of different scales and fiber orientation are presented. A parametric study based on the fiber aspect ratio, volume fraction and interaction coefficient is used to explore the effects of fiber on system performance. The effects of different inlet temperatures on the stress are also discussed. The present results may elucidate the relationship of the three scales, and exhibit the possibility for developing a meaningful rheological modeling of the polymeric flow of fiber suspensions at the multi-level for industrial application.     

Numerical simulation of three‐dimensional fiber orientation in injection molding including fountain flow effect

It is essential to predict the nature of flow field inside mold and flow‐induced variation of fiber orientation for effective design of short fiber reinforced plastic parts. In this investigation, numerical simulations of flow field and three‐dimensional fiber orientation were carried out in special consideration of fountain flow effect. Fiber orientation distribution was described using the second‐order orientation tensor. Fiber interaction was modeled using the interaction coefficient C_I. Three closure approximations, hybrid, modified hybrid, and closure equation for C_I=0, were selected for determination of the fiber orientation. The fiber orientation routine was incorporated into a previously developed program of injection mold filling (CAMPmold), which was based on the fixed‐grid finite element/finite difference method assuming the Hele‐Shaw flow. For consideration of the fountain flow effect, simplified deformation behavior of fountain flow was employed to obtain the initial condition for fiber orientation in the flow front region. Comparisons with experimental results available in the literature were made for film‐gated strip and centergated disk cavities. It was found that the orientation components near the wall were were accurately predicted by considering the fountain flow effect. Test simulations were also carried out for the filling analysis of a practical part, and it was shown that the currently developed numerical algorithm can be effectively used for the prediction of fiber orientation distribution in complex parts.     

纤维增强复合材料的力学性能预测的数值模拟

纤维增强复合材料的力学性能和热物理性能依赖于纤维的取向状态.在注射成型过程中纤维最终的取向状态依赖于充填过程的速度场,因此最终的产品性质依赖于成型的详细过程.研究发现,注塑成型制品的结构呈层状分布,层数依赖于模具几何和成型条件,不过大多数的结构在成型表面为沿流动方向取向,而在中心层为横向排列,有时在制件表面还有一层薄的介于二者之间排列的取向层.本文主要给出两个简单模型中纤维取向预测的理论和数值方法,这两个模型分别为:中心浇口圆盘和边浇口长条.     

Interface development and encapsulation in simultaneous coinjection molding of disk. II. Two‐dimensional simulation and experiment

Two‐dimensional simulation and experimental studies of flow‐rate‐controlled coinjection molding were carried out. Skin polymer was injected first, and then both skin and core polymers were injected simultaneously into a center‐gated disk cavity through a two‐channel nozzle to obtain an encapsulated sandwich structure. The physical modeling and simulation developed, reported in Part I of this series, were based on the Hele–Shaw approximation and the kinematics of the interface to describe the multilayer flow, and the interface development was used to predict the skin/core distribution in the moldings. The effects of rheological properties and processing conditions on the material distribution, penetration behavior, and breakthrough phenomena were investigated. The predicted and measured results were found to be in a good agreement. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 2310–2318, 2003     

Fibre orientation distribution in turbulent fibre suspensions flowing through an axisymmetric contraction

The Reynolds averaged Navier–Stokes equation was solved numerically with the Reynolds stress model to get the mean fluid velocity and the turbulent kinetic energy in turbulent fibre suspensions flowing through an axisymmetric contraction. The fluctuating fluid velocity was represented as a Fourier series with random coefficients. Then the slender‐body theory was used to predict the fibre orientation distribution and orientation tensor. Some numerical results are compared with the experimental ones in the turbulent fibre suspensions flowing through a contraction with a rectangular cross‐section. The results show that the fibres with high aspect ratio tend to align its principal axis with the flow direction much easier. High contraction ratio makes the fibre alignment with the flow direction much easier. The contraction ratio has a strong effect on the fibre orientation distribution. Only a small part of the fibre is aligned with the flow direction in the inlet region, while most fibres are aligned with the flow direction when they approach to exit. The fibres are aligned with the flow direction rapidly in the inlet region, after that the fibre orientations change little in the most of the downstream region. The fibres with high aspect ratio are aligned with the flow direction faster when they enter the contraction. The randomising effect of the turbulence becomes significant in the downstream region because of the high turbulent intensity.     

Experimental study and calculations of short glass fiber orientation in a center gated molded disc

Short glass fiber orientation in a center gated molded disc of polyamide is studied using optical microscopy techniques. The very different orientation between the core and the surface of the molding is quantified with an orientation function. The influence of the molding conditions is investigated. A numerical scheme is used for modeling the mold filling with a viscous melted polymer. A computation method is introduced to describe the fiber movement during the flow. The theoretical results are in good agreement with the experimental ones. In particular, the very different orientation between the skin and the core of the disc is well predicted.     

Numerical simulation of fibre suspension flow through an axisymmetric contraction and expansion passages by Brownian configuration field method

In this paper, the finite element method is combined with the Brownian configuration field (BFC) method to simulate the fibre suspension flow in axisymmetric contraction and expansion passages. In order to solve for the high stress at high concentration, the discrete adaptive viscoelastic stress splitting (DAVSS) method is employed. For the axisymmetric contraction and expansion passages with different geometry ratios, the results obtained are compared to available constitutive models and experiments. The predicted vortex length for dilute suspensions agrees well with experimental data in literature. Our numerical results show clearly the effect on vortex enhancement with increase of the volume fractions and the aspect ratios. Effect of aspect ratio of fibres on the vortex length is also studied. It is found that for the lower expansion ratio flows the vortex dimension in the corner region is fairly independent of fibre concentration and aspect ratio of fibres while the said vortex dimension increases with the increase of fibre concentration for contraction flows. The finding suggests that the aligned fibre approximation traditionally employed in previous work does not exactly describe the effect of fibre motion, and the present BFC method is deemed more suitable for the flow of dilute fibre suspensions. In terms of numerics, the employment of DAVSS enhances numerical stability in the presence of high concentration of fibre in the flow.     

Flow induced fiber orientation in compression molded glass mat thermoplastics

This study examines how the mechanical properties in GMT are affected by axisymmetric flow during compression molding. Two types of GMT with different architecture are used, swirled mat and short fiber GMT. Tree different grades are tested for each fiber architecture 20, 30, and 40% fiber content by weight. These are in principle the grades of GMT commercially available today. It is found that the flow reduced the tensile strength by 30 to 50% and the tensile modulus up to 30% in the flow direction. The reduction in mechanical properties, which is mainly caused by flow‐induced fiber orientation, is larger at high fiber contents. The study also showed that there is no major difference in behavior between swirled mat and short fiber GMT regarding flow induced fiber orientation.     

A new differential pressure flow meter for measurement of human breath flow: Simulation and experimental investigation

The development and performance characterization of a new differential pressure‐based flow meter for human breath measurements is presented in this article. The device, called a “Confined Pitot Tube,” is comprised of a pipe with an elliptically shaped expansion cavity located in the pipe center, and an elliptical disk inside the expansion cavity. The elliptical disk, named Pitot Tube, is exchangeable, and has different diameters, which are smaller than the diameter of the elliptical cavity. The gap between the disk and the cavity allows the flow of human breath to pass through. The disk causes an obstruction in the flow inside the pipe, but the elliptical cavity provides an expansion for the flow to circulate around the disk, decreasing the overall flow resistance. We characterize the new sensor flow experimentally and theoretically, using Comsol Multiphysics^® software with laminar and turbulent models. We also validate the sensor, using inhalation and exhalation tests and a reference method. © 2016 American Institute of Chemical Engineers AIChE J, 62: 956–964, 2016     

Velocity Profiles of Suspension Flows through an Abrupt Contraction Measured by Magnetic Resonance Imaging

Velocity profiles in steady flows of fluid/particle mixtures through a duct with an abrupt contraction were measured by magnetic resonance imaging. Aqueous solutions of carboxymethyl cellulose containing particles, including spheres, disk‐like particles, and short fibers, at high volume fractions were used. As a result, a plug‐like velocity profile was observed in a straight duct flow for every suspension, but the velocity profile depends on the particle shape at contraction. Disk‐like particles caused an unsteady flow, and short fibers caused a concave shape in the velocity profile near the centerline upstream of the contraction. Spheres did not affect the flow field. The concave profile became obvious with increased volume fraction of fiber. This result is caused by the larger elongational viscosity of the fiber suspension near the centerline of the channel, as compared with that of the sphere suspension.     

Numerical Modelling of the Flow of Fibre Suspensions through a Planar Contraction

This study presents results of numerical simulations of the flow of fibre suspensions in a Newtonian fluid through a 4:1 planar contraction. Two approaches are adopted to determine the fibre orientation. The first one uses orientation tensors defined as dyadic products of the orientation vector, while the second one is based on the fibre aligned assumption. An implicit time discretization scheme and a mixed finite element method based on the introduction of the rate of deformation tensor as an additional unknown are used to obtain the steady‐state flow. The numerical technique we use allows us to examine the flow of fibre suspensions in both dilute and semi‐dilute regimes at high values of the parameters controlling inertial and fibre effects. The predicted flow patterns and fibre orientation are discussed, and a systematic comparison between the predictions of the two approaches is presented.     

Effects of abrupt expansion geometries on flow‐induced fiber orientation and concentration distributions in slit channel flows of fiber suspensions

Flow‐induced fiber orientation and concentration distributions were measured in channel flows of fiber suspension. The test fluids used are a concentrated fiber suspension (CFS), a semidilute one (SDFS), and a dilute one (DFS). The channel has a thin slit geometry with a 1:16 expansion. In the present work, fiber orientation and concentration distributions are quantitatively evaluated by direct observation of fibers even in the CFS flow. It is found that the weak fiber–fiber interaction of the SDFS largely affects the fiber orientation in the flow with a sudden change such as in the expansion flow, while it is ineffective upon the fiber orientation in the flow without a sudden change such as in the far downstream region. Fiber concentration in the CFS has a flat distribution over a channel width in both the entrance region of the expansion and the downstream region. However, fiber concentration distributions in the SDFS and the DFS have a small and a large peak near the sidewall in the entrance region, respectively, due to the fiber‐wall interaction at the channel wall. These peaks, however, disappeared in the far downstream region after the fibers passed through the expansion. POLYM. COMPOS., 26:660–670, 2005. © 2005 Society of Plastics Engineers.     

纤维增强塑料的充模流动和纤维取向的耦合仿真模型

分析充模流动、纤维取向耦合仿真的特点,在此基础上提出充模流动、纤维取向耦合仿真模型,可对充填和后充填阶段的可压缩流体的非对称流动,以及由于熔体流动引起的三维纤维取向行为进行统一建模,并且两者相互耦合,在耦合程度上考虑了由于增强纤维存在并且取向引起的熔体流动类型、流变学性质和本构方程的变化.     

Improved model of orthotropic closure approximation for flow induced fiber orientation

We developed improved models (called ORW and ORW3) of existing “orthotropic fitted” closure approximations (ORF or ORL) for use with a wide range of fiber‐fiber interaction coefficients. Closure approximation refers to the approximation of a higher order tensor in terms of a lower order tensor. Principal values of the 4th order tensor are assumed in terms of polynomial expansions of the eigenvalues of the 2nd order tensor. Unknown parameters are determined by a least‐square fitting technique with assumed exact solutions. Flow data for the optimal fitting were designed to cover the entire domain of the orientation triangle as uniformly as possible to eliminate non‐physical oscillation. Shear/biaxial stretching combined flow turns out to play an important role in covering the orientation triangle, thereby increasing the accuracy of fiber orientation prediction. When tested for a variety of flow cases, neither ORW nor ORW3 shows any of the non‐physical oscillatory behaviors that ORF and ORL frequently suffer from.     

纤维悬浮聚合物熔体中纤维影响的数值模拟

采用一种多尺度模型研究了纤维悬浮聚合物熔体的流动过程,通过宏观流体的流动状态、纤维所在尺度上的纤维取向表征和聚合物溶液大分子哑铃模型尺度上的哑铃概率分布三尺度信息,实现了纤维悬浮聚合物熔体流动控制方程和本构关系的三尺度共同表征。使用SIMPLER-FDMS算法对多尺度控制方程组进行了求解,并通过4∶1等温平板收缩流的数值模拟验证了该多尺度模型的有效性。通过对纤维浓度、纤维间相互作用以及纤维长径比的分析,研究了纤维参数对聚合物基熔体悬浮体系及纤维取向的影响。     

纸桨泵叶轮中纤维悬浮湍流的流动特性(英文)

A numerical method for predicting fiber orientation is presented to explore the flow properties of turbu-lent fiber suspension flowing through a stock pump impeller. The Fokker-Planck equation is used to describe the distribution of fiber orientation. The effect of flow-fiber coupling is considered by modifying the constitutive mode. The three-dimensional orientation distribution function is formulated and the corresponding equations are solved in terms of second-order and fourth-order orientation tensors. The evolution of fiber orientation, flow velocity and pressure, additional shear stress and normal stress difference are presented. The results show that the evolutions of fiber orientation are different along different streamlines. The velocity and its gradient are large in the concave wall region, while they are very small in the convex wall region. The additional shear stress and normal stress difference are large in the inlet and concave wall regions, and moderate in the mid-region, while they are almost zero in most downstream regions. The non-equilibrium fiber orientation distribution is dominant at the inlet and the concave wall regions. The flow will consume more energy to overcome the additional shearing losses due to fibers at the inlet and the concave wall regions. The change of flow rates has effect on the distribution of additional shear stress and normal stress difference. The flow structure in the inlet and concave wall regions is essential in the resultant rheological properties of the fiber suspension through the stock pump impeller, which will directly affect the flow efficiency of the fiber suspension through the impeller.     

Mechanical properties of glass fiber reinforced polypropylene injection molded with a rotation mold

A special mold (Rotation, Compression, and Expansion Mold) was used to impose a controlled shear action during injection molding of short glass fiber reinforced polypropylene discs. This was achieved by superimposing an external rotation to the pressure‐driven advancing flow front during the mold filling stage. Central gated discs were molded with different cavity rotation velocities, inducing distinct levels of fiber orientation through the thickness. The mechanical behavior of the moldings was assessed, in tensile and flexural modes on specimens cut at different locations along the flow path. Complete discs were also tested in four‐point flexural and in impact tests. The respective results are analyzed and discussed in terms of relationships between the developed fiber orientation level and the mechanical properties. The experimental results confirm that mechanical properties of the moldings depend strongly on fiber orientation and can thus be tailored by the imposed rotation during molding. POLYM. ENG. SCI. 46:1598–1607, 2006. © 2006 Society of Plastics Engineers.