Numerical simulation of fiber orientation distribution in round turbulent jet of fiber suspension

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 a round turbulent jet of fiber suspension. The fluctuating fluid velocity was described as a Fourier series with random coefficients. Then the slender-body theory was used to calculate the fiber orientation distribution and orientation tensor. Numerical results of mean axial velocity and turbulent shear stress along the lateral direction were validated by comparing with the experimental ones. The results show that most fibers are aligned with the flow direction as they go downstream, and fibers are more aligned with the flow direction within the region near the jet core. The fibers with high aspect ratio tend much easier to align with the flow direction, and the fiber orientation distribution is not sensitive to fiber aspect ratio when fiber aspect ratio is larger than 5. Fiber density has no obvious influence on the fiber orientation distribution and fiber orientation tensor. The randomizing effect of turbulence is insignificant in the regions near outside and jet core, and becomes significant in the region between outside and jet core. The randomizing effect increases with the increasing of the distance from the jet exit. Different components of fiber orientation tensor show a similar distribution pattern.     

Rheological behavior and fiber orientation in slit flow of fiber reinforced thermoplastics

The flow behavior and fiber orientation in slit flow of a short fiber reinforced thermoplastic composite melt are investigated. A slit die with adjustable gap and interchangeable entrance geometries was designed and built. The slit die is fed by a single screw extruder. The bulk viscosity is calculated from the axial pressure profiles measured using three flush mounted pressure transducers. The effect of entrance geometry and gap dimensions on the fiber orientation and bulk flow behavior is specifically considered. A skin-core composite fiber orientation is observed in the thickness direction. Fibers are oriented in the flow direction and parallel to the walls in the skin region irrespective of the entrance geometry. Different fiber orientation distributions in the core region can be realized by using different entrance geometries. However, the changes in the core fiber orientation are not fully reflected by the measured viscosities, due to highly oriented skin layer. Exit pressures obtained by extrapolation of linear pressure profiles are found to be all positive, but dependent on the die geometry and entrance conditions, even for the unfilled melts.     

Flow visualization of fiber suspensions

A visualization study of the flow of fiber-filled resin through cylindrically convergent channels has been conducted. Epoxy resins filled with glass fibers were tested to simulate the flows experienced during the processing of fiber reinforced thermoplastics. Specific phenomena which have been investigated include the kinematics, orientation of the suspended fibers, formation of possible unwanted stagnant eddies at the entrance of the channel, and the fiber length degradation. It was found that the extensional flow in the convergent channel plays an important role in orienting the fibers.     

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.     

Prediction of fiber orientation in a rotating compressing and expanding mold

In the rotating/compressing/expanding mold (RCEM), one mold wall can expand, compress, and rotate during injection molding, thus offering opportunities to control the thermomechanical history of a polymer and its microstructure. A computer simulation of flow and fiber orientation in RCEM was developed. The predictive model extends the generalized Hele‐Shaw formulation to account for compression/expansion and rotation of the mold wall, and uses the Folgar–Tucker model for fiber orientation predictions. A 20% GF polypropylene was molded under various molding conditions. The predicted fiber orientation distributions were compared with experiments. The model compares favorably with experiments, provided that the fiber orientation equation is modified by a strain‐reduction factor that slows the transient development of fiber alignment. The effect of fountain flow on orientation must also be included to correctly predict fiber orientation near the mold walls, mainly for the case of stationary and linear motions of the mold surface. Compression or expansion of the mold has only a small effect on fiber orientation, but rotation of the mold dramatically changes the orientation, causing fibers to align in the tangential direction across the entire thickness of the molding. This rotation action perturbs the fountain flow and becomes the dominant factor affecting fiber alignment across the entire cavity thickness. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers.     

Flow induced fiber orientation in an expanding channel tubing dies

In the application of plastic pipes for fluid transport and for the protection of underground electrical cables, it is desirable to improve mechanical properties, particularly in the hoop direction. The use of orientable reinforcing particles such as chopped glass fibers could make possible such an improvement if the orientation of the fibers could be controlled. While conventional pipe extrusion dies tend to promote axial fiber orientation, the use of an expanding channel die has been proposed to produce a preferential hoop orientation of fibers. In this paper, a theoretical model of the flow of a fiber suspension through an expanding channel die that predicts the fiber orientation distribution at the die exit is described. The effects of Theological properties and die geometry on the final fiber orientation distribution are predicted. The results of an experimental study of fiber orientation in pipe extruded using an expanding channel die are shown to be in agreement with the theoretical predictions.     

Numerical investigation of three-dimensional fiber suspension flow by using finite volume method

Fiber suspension flow is common in many industrial processes like papermaking and fiber-reinforcing polymer-based material forming. The investigation of the mechanism of fiber suspension flow is of significant importance, since the orientation distribution of fibers directly influences the mechanical and physical properties of the final products. A numerical methodology based on the finite volume method is presented in the study to simulate three-dimensional fiber suspension flow within complex flow field. The evolution of fiber orientation is described using different formulations including FT model and RSC model. The pressure implicit with splitting of operators algorithm is adopted to avoid oscillations in the calculation. A laminate structure of fiber orientation including the shell layer, the transition layer and the core layer along radial direction within a center-gated disk flow channel is predicted through a three-dimensional simulation, which agrees well with Mazahir’s experimental results. The evolution of fiber orientation during the filling process within the complex flow field is further discussed. The mathematical model and numerical method proposed in the study can be successfully adopted to predict fiber suspension flow patterns and hence to reveal the fiber orientation mechanism.     

Investigation of fiber orientation states in injection‐compression molded short‐fiber‐reinforced thermoplastics

Injection‐compression molding (ICM) has received increased attention because of its advantages over conventional injection molding (CIM). This article aims to investigate the effects of five dominating ICM processing parameters on fiber orientation in short‐fiber‐reinforced polypropylene (SFR‐PP) parts. A five‐layer structure of fiber orientation is found across the thickness under most conditions in ICM parts. This is quite different from the fiber orientation patterns in CIM parts. The fibers orient orderly along the flow direction in the shell region, whereas most fibers arrange randomly in the skin and the core regions. Additionally, the fiber orientation changes in the width direction, with most fibers arranging orderly along the flow direction at positions near the mold cavity wall. The results also show that the compression force, compression distance, and compression speed play important roles in determining the fiber states. Thicker shell regions, in which most fibers orient remarkably along the flow direction, can be obtained under larger compression force or compression speed. Moreover, the delay time has an obvious effect on the fiber orientation at positions far from the gate. However, the effect of compression time is found to be negligible. POLYM. COMPOS., 31:1899–1908, 2010. © 2010 Society of Plastics Engineers.     

Simple tools for fiber orientation prediction in industrial practice

In this paper, the two origins of the preferred orientation of fibers are first reviewed. We then propose a definition of what to call an oriented fiber from a practical point of view in the cementitious material field. Considering typical industrial flows and materials, we identify the dominant phenomena and orientation characteristic time involved in the fiber orientation process in the construction industry. We show that shear induced fiber orientation is almost instantaneous at the time scale of a typical casting process. We moreover emphasize the fact that shear induced orientation is far stronger in the case of fluid materials such as self compacting concretes. The proposed approach is validated on experimental measurements in a simple channel flow. Finally, a semi-empirical relation allowing for the prediction of the average orientation factor in a section as a function of the rheological behavior, the length of the fibers and the geometry of the element to be cast is proposed.     

Numerical analysis of injection molding of glass fiber reinforced thermoplastics. Part 2: Fiber orientation

Numerical predictions of fiber orientation during injection molding of fiber-filled thermoplastics are compared to measurements. The numerical work successfully describes the flow of fiber-filled plastic during injection molding, using finite-difference solutions for the transport equations and marker particles to track the flow front. The flow is modeled as a 2-D, non-isothermal, free-surface flow with a new viscosity model dependent upon temperature, pressure, and fiber concentration. The fiber orientation is based upon solution to the Fokker-Planke equation. The comparison demonstrates fair agreement between predicted fiber orientation and experimental results for slow and fast injection speeds. For the slow speed case at 10 and 20 wt% fibers, the numerical and experimental works show that the fibers are more random at the flow front than at the centerline, and that the fibers become more aligned as they flow from the gate to the midstream region. At fast injection speeds, the agreement between the numerical and experimental works is not as good as at slow injection speed. Possible explanations for the discrepancies are that the flow is assumed to be simple shear when injection molding is known to be a pressure-driven flow, the fibers have an initial orientation for the runner rather than the assumed random orientation, the fibers that were displayed from the camera were more oriented just behind the flow front (owing to the fast injection speed), and the orientation requires more than a 2-D video image to represent a 3-D fiber orientation.     

Natural fiber suspensions in thermoplastic polymers. I. Analysis of fiber damage during processing

The final properties of the composites materials are strongly dependent on the residual aspect ratio, orientation, and distribution of the fibers, which are determined by the processing conditions. Present work is a systematic study of the influence of natural fiber concentration on its damage during all the steps involved in the composite compounding. The system under study is cellulose fiber‐reinforced polypropylene. The fiber geometrical parameters—length, diameter, and aspect ratio—are measured, and their statistical distributions are assessed for different concentrations. It is found that the higher the fiber concentration, the lower the fiber damage. These results evidence a difference in behavior between the damage of flexible natural fiber and rigid ones. The results are analyzed in terms of fiber concentration regimes, fiber–fiber interaction, flexibility, and entanglements. Two competitive mechanisms of the fiber interaction are proposed for explaining the fiber damage behavior during the flow of the flexible natural fiber suspensions. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 2501–2506, 2007     

A numerical simulation of short fiber orientation in compression molding

A computer simulation has been developed to predict the orientation of fibers in a thin, flat part that is compression molded from sheet molding compound. The simulation combines a finite element/control volume simulation of the mold filling flow, a second order tensor representation of the fiber orientation state and a finite element calculation for the transient orientation problem. Sample results and comparison with experiments are presented. Predictions compare favorably with experiments on SMC (sheet molding compound) plaques and a model suspension of nylon fibers and silicon oil.     

Rheology of fiber filled polymer melts: Role of fiber‐fiber interactions and polymer‐fiber coupling

An experimental study and a numerical modeling analysis are carried out to examine the effects of fiber‐fiber interactions and coupling between fiber orientation and polymer chains conformation on the rheological properties of fiber suspensions. The experimental study allowed examination of large fiber volume fractions up to 35% over a range of shear rates that spans eight decades. This study confirmed already known results and led to new ones. In particular, a peak in the steady shear viscosity at the low shear rate region is observed at large volume fractions. Furthermore, new results regarding the applicability of the Cox‐Merz rule, the behavior of the damping factor, and the end pressure drops are reported, and physical interpretations are proposed. The results of the numerical modeling showed that it is necessary to account for the polymer‐fiber coupling factor to obtain a good fit between the model predictions and the experimental measurements. Comparisons between the model predictions and the experimental measurements allowed study of the variation of the parameters that govern the fiber‐fiber interactions and the polymer‐fiber coupling with the properties of the suspension and the flow. POLYM. ENG. SCI., 45:385–399, 2005. © 2005 Society of Plastics Engineers     

Fiber orientation and mechanical properties of short-fiber-reinforced injection-molded composites: Simulated and experimental results

A numerical simulation is presented that combines the flow simulation during injection molding with an efficient algorithm for predicting the orientation of short fibers in thin composite parts. Fiber-orientation state is represented in terms of a second-order orientation tensor. Fiber-fiber interactions are modeled by means of an isotropic rotary diffusion. The simulation predicts flow-aligned fiber orientation (shell region)near the surface with transversely aligned (core region) fibers in the vicinity of the mid-plane. The effects of part thickness and injection speed on fiber orientation are analyzed. Experimental measurements of fiber orientation in plaque-shaped parts for three different combinations of cavity thickness and injection speed are reported. It is found that gapwise-converging flow due to the growing layer of solidified polymer near the walls tends to flow-align the fibers near the entrance, whereas near the melt front, gapwise-diverging flow due to the diminishing solid layer tends to lign the fibers transverse to the flow. The effect of this gapwise-converging-diverging flow is found to be especially significant for thin parts molded at slower injection speeds, which have a proportionately thicker layer of solidified polymer during the filling process. If the fiber orientation is known, predictions of the anisotropic tensile moduli and thermal-expansion coefficients of the composite are obtained by using the equations for unidirectional composites and taking an orientation average. These predictions are found to agree reasonably well with corresponding experimental measurements.     

Numerical prediction of three-dimensional fiber orientation in Hele-Shaw flows

A numerical technique is developed to determine the three-dimensional fiber orientation in complex flows. The fiber orientation state is specified in terms of orientation tensors, which are used in several constitutive models. This method is applied to quasi-steady state Hele-Shaw flows in order to predict the flow-induced fiber orientation during injection molding at zero volume fraction limit. At the inlet, a number of fibers are introduced at a specified rate into the flow and each fiber location is traced during the mold filling. Along these determined paths, the independent components of fourth order orientation tensors are solved, describing the orientation state. The numerical grid generation technique, which is suitable for complex mold shapes, is employed for the flow solution. Orientation ellipsoids are calculated from the second order tensors and are used to present the fiber orientation results. The numerical solutions are obtained for channel and converging flows. Planar, longitudinal, and transverse orientation results are generated from the orthogonal projections of the orientation ellipsoids.     

Polyamide 6—long glass fiber injection moldings

The injection molding ability of long glass fiber reinforced polyamide pellets was studied. The injection moldable materials were produced by a melt impregnation process of continuous fiber rovings. The rovings were chopped to pellets of 9 mm length. Chopped pellets with a variation in the degree of impregnation and fiber concentration were studied. The injection molded samples were analyzed for fiber concentration, fiber length, and fiber orientation. Dumbbell-shaped tensile bars were made to evaluate the mechanical properties. The fibers in the tensile bars had a high orientation in the flow direction and minor fiber concentration gradients were observed. The fiber lengths decreased with fiber concentration from 1.6 mm for a 2 vol% to 0.6 mm for a 25 vol% system. The tensile and impact properties increased considerably with fiber concentration. A low degree of impregnation in the pellets of the fibers resulted in somewhat lower tensile and impact properties.     

Dynamic simulation of microstructure and rheology of fiber suspensions

A numerical simulation method has been developed to predict the motion of fiber suspensions in various flows by using the particle simulation method (PSM), in which a fiber is modeled by an array of spheres. The hydrodynamic interaction among fibers is considered by decomposing into intra-fiber and inter-fiber interactions. For the intra-fiber case, the many-body problem is solved by calculating the mobility matrix for each fiber to obtain the hydrodynamic force and torque exerted on each sphere. For the inter-fiber case, only the near-field lubrication force is considered between spheres belonging to different fibers. The methodology was applied to predicting the microstructure and rheological properties of rigid fiber suspensions in simple shear flow and fiber orientation in two-dimensional diverging flow by combining this method with the finite element method (FEM). In the former, the overshoot of suspension viscosity, due to the transient change of the microstructure, was observed in semi-dilute to concentrated systems. In the latter, the calculated fiber orientations agreed with expectations of theory.     

Dynamics of semi-flexible and breakable fibers under Poiseuille flow

In the processing of fiber-reinforced polymer composites, especially in injection molding, the fiber's orientation, length, and distribution vary depending on the location of the channel flow and its properties, which affects the performance of final products. To investigate the intricate behavior of fiber suspensions under Poiseuille flow, we used the hybrid simulation approach, multiparticle collision dynamics–molecular dynamics (MPC-MD), which takes hydrodynamic interactions and fiber properties (strength, flexibility) into account. For non-breakable and rodlike fibers, fibers align well along the flow direction while showing more alignment near the wall. As fiber becomes breakable and/or flexible, the length and orientation of fibers strongly depend on their properties. The interesting phenomenon is specifically seen for breakable and semiflexible fibers, where the orientation of the fiber exhibits non-monotonic behavior depending on the flow rate. This complex behavior highlights the importance of comprehending the dynamics of many types of fibers and necessitates research into the best conditions for injection molding.     

The viscosity of fiber suspensions at low fiber volume fractions

The viscosities of suspensions of glass fibers in an aqueous solution of sucrose have been studied by use of a capillary viscometer. In the aligned condition in the capillary, the viscosity depends little on shear rate within the range studied or on fiber length, but increases with increasing volume fraction of the fibers. The entrance effect was found to depend strongly on fiber volume fraction and fiber length: this indicates that the suspensions are relatively resistant to flow during the initial stages while alignment takes place.     

Measurement of fiber and matrix orientations in fiber reinforced composites

Short glass fiber reinforced polypropylene was employed in a study to determine the effect of molding and mold design variables on the distrubution of fibers and their orientations, and consequently, on the distributions of mechanical properties in the molded article. In this paper, a variety of experimental techniques were employed to evaluate the distributions of fibers and their orientations. Moreover, techniques were developed to evaluate the orientation and crystallization of the matrix. The results yield significant information regarding the development and control of both the microstructure and the properties of short fiber reinforced composites.