Simulations of a full three‐dimensional packing process and flow‐induced stresses in injection molding

Numerical investigations of a full three‐dimensional (3D) packing process and flow‐induced stresses are presented. The model was constructed on the basis of a 3D nonisothermal weakly compressible viscoelastic flow model combined with extended pom‐pom (XPP) constitutive and Tait state equations. A hybrid finite element method (FEM)–finite volume method (FVM) is proposed for solving this model. The momentum equations were solved by the FEM, in which a discrete elastic viscous stress split scheme was used to overcome the elastic stress instability, and an implicit scheme of iterative weakly compressible Crank–Nicolson‐based split scheme was used to avoid the Ladyshenskaya–Babu?ka–Brezzi condition. The energy and XPP equations were solved by the FVM, in which an upwind scheme was used for the strongly convection‐dominated problem of the energy equation. Subsequently, the validity of the proposed method was verified by the benchmark problem, and a full 3D packing process and flow‐induced stresses were simulated. The pressure and stresses distributions were studied in the packing process and were in agreement with the results of the literature and experiments in tendency. We particularly focused on the effects of the elasticity and pressure on the flow‐induced stresses. The numerical results show that normal stress differences decreased with incremental Weissenberg number and increased with incremental holding pressure. The research results had a certain reference value for improving the properties of products in actual production processes. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

3‐D full‐loop simulation of an industrial‐scale circulating fluidized‐bed boiler

Three‐dimensional (3‐D) simulations using an Eulerian multiphase model were employed to explore flow behaviors in a full‐loop industrial‐scale CFB boiler with and without fluidized‐bed heat exchanger (FBHE), where three solids phases were employed to roughly represent the polydisperse behavior of particles. First, a simulation of the boiler without FBHE is implemented to evaluate drag models, in terms of pressure profiles, mixing behaviors, radial velocity profiles, etc. Compared to the conventional model, the simulation using the energy‐minimization multiscale (EMMS) model successfully predicts the pressure profile of the furnace. Then, such method is used to simulate the boiler with FBHE. The simulation shows that solid inventory in the furnace is underpredicted and reduced with an increase of the valve opening, probably due to the underevaluated drag for FBHE flows. It is suggested to improve EMMS model which is now based on a single set of operating parameters to match with the full‐loop system. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1108–1117, 2013     

A new equation for predicting electrical conductivity of carbon‐filled polymer composites used for bipolar plates of fuel cells

In this article, a statistical‐thermodynamic formula based on a new approach has been developed to predict electrical conductivity of carbon‐filled composites used for bipolar plate of proton exchange membrane fuel cell. In this model, based on percolation threshold phenomenon, it is assumed that the relationship between electrical conductivity of composite and filler volume fraction follows a sigmoidal equation. Afterwards, the four effective factors on composite conductivity including filler electrical conductivity, filler aspect ratio, wettability, as well as interface contact resistance are replaced upon constant parameters of sigmoidal function. In order to test the model, some single‐filler composites have been manufactured by using the phenolic resin as binder and graphite (G), expanded graphite (EG), and carbon fiber (CF) as fillers. The fitting quality is measured by R‐square, adjusted R‐square, SSE, and RMSE parameters. The results showed that there is a noteworthy agreement between the model and the experimental data. Compared to the other models, this model can be used for more types of fillers. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Effects of periodic and non‐periodic chaotic mixing on morphology development of immiscible polymer blends

The effects of periodic and non‐periodic chaotic mixing on the morphology development in the blending of polypropylene as dispersed phase and polyamide 6 as continuous phase in a 2D batch chaotic mixer were investigated with experimental and computational fluid dynamic (CFD) methods. The rotor motions were delivered in steady, periodic (sine waveform and square waveform), and non‐periodic (recursive protocol (RP) and restricted random sequence (RRS)) manners. The mixing efficiency was evaluated with flow number, Poincare map, morphology, droplet size and its distribution. Compared with the sine waveform, RP waveform could eliminate the island structures which existed in the flow domains and its corresponding spatial stretching distribution was more uniform. The recursively generated flow using RP lead to higher mixing efficiency and smaller droplet size with narrow distribution. However, the performance of RRS was ordinary even worse due to its random sequence.© 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Design methodology for barrier‐based two phase flow distributor

The barrier‐based distributor is a multiphase flow distributor for a multichannel microreactor which assures flow uniformity and prevents channeling between the two phases. For N number of reaction channels, the barrier‐based distributor consists of a gas manifold, a liquid manifold, N barrier channels for the gas, N barrier channels for the liquid, and N mixers for mixing the phases before the reaction channels. The flow distribution is studied numerically using a method based on the hydraulic resistive networks (RN). The single phase hydraulic RN model (Commenge et al., 2002;48:345–358) is extended for two phases gas‐liquid Taylor flow. For Re_GL <30, the accuracy for the model was above 90%. The developed‐model was used to study the effects of fabrication tolerance and barrier channel dimensions. A design methodology has been proposed as an algorithm to determine the required hydraulic resistance in the barrier channels and their dimensions. This methodology is demonstrated using a numerical example. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

A finite piece method for simulating polymer melt flows in extrusion sheet dies

A finite piece method is proposed to simulate three‐dimensional slit flows in extrusion sheet dies in this paper. The simulations concern incompressible fluids obeying different constitutive equations: generalized Newtonian (Carreau‐Yasuda law), and viscoelastic Phan‐Thien Tanner (PTT) models. Numerical simulations are carried out for the isothermal and nonisothermal flows of polymer melt through sheet dies. The Picard iteration method is utilized to solve nonlinear equations. The results of the finite piece method are compared with the three‐dimensional (3D) finite element method (FEM) simulation and experiments. At the die exit, the relative error of the volumetric flow between the finite piece method and the 3D FEM is below 1.2%. The discrepancy of the pressure distributions does not exceed 6%. The Maximum error of the uniformity index between the simulations and experiments is about 2.3%. It shows that the solution accuracy of the finite piece method is excellent, and a substantial amount of computing time and memory requirement can be saved. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Transient computational fluid dynamics modeling of pervaporation separation of aromatic/aliphatic hydrocarbon mixtures using polymer composite membrane

Pervaporation (PV) separation of toluene/n‐heptane mixtures was studied experimentally and theoretically by means of a molecular surface engineering (MSE) polymer composite membrane. A comprehensive mathematical model was developed to predict unsteady state transport of toluene and n‐heptane (nC₇) through the membrane. Conservation equations including continuity, and heat transfer equations were solved using finite element method (FEM). Computational fluid dynamics (CFD) technique was applied to solve the model equations. The model was then verified with PV experimental data. The simulation results were in good agreement with the experimental data. The simulation results revealed that the proposed model could provide a general simulation of transport in the PV process. POLYM. ENG. SCI., 2013. © 2012 Society of Plastics Engineers     

Calibration of one‐dimensional flow setup used for estimating fabric permeability using three different reference media

Experimental estimation of the permeability of reinforcement fabrics is very important in conducting accurate mold‐filling simulations for liquid composite molding (LCM) processes employed to manufacture polymer matrix composites. In this study, the one‐dimensional (1D) flow based permeability measuring setup was calibrated for the first time using three different reference media: an aluminum block with drilled parallel holes, a lattice of 3D unit cells created using rapid prototyping, and carbon fabric used in the recently concluded permeability bench‐mark study [Vernet N, et al. Compos Part A, 61, 172 (2014)]. The steady‐state permeability was estimated for all the three cases while the transient permeability was estimated only for the lattice‐type and carbon fabric media. The carbon‐fabric results were presented as the transient and steady‐state permeabilities for three different directions of 0°, 45°, and 90°, and the in‐plane principal permeability components were calculated using the correlations for anisotropic fabrics. The results for the aluminum‐plate and lattice‐like media were compared with the previous numerical and experimental studies and good agreement was observed. To validating the carbon‐fabric results, the experimental permeability was compared with two different analytical permeabilities for dual‐scale porous media [Papathanasiou, Int. J. Multiphase Flow, 27 ( 8 ), 1451 (2001) and K.M. Pillai and S.G. Advani, Transport Porous Med., 21 ( 1 ), 1 (1995)], and a good agreement with experimental results established the accuracy of our 1D flow setup. The study raises some important questions on the permeability benchmark study conducted recently [Vernet N, et al. Compos Part A, 61, 172 (2014)]. POLYM. COMPOS., 37:925–935, 2016. © 2014 Society of Plastics Engineers     

Bubble behavior in corrugated‐wall bubbling fluidized beds—Experiments and CFD simulations

A new concept to harness bubble dynamics in bubbling fluidization of Geldart D particles was proposed. Various geometrical declinations of a cold‐prototype corrugated‐wall bubbling fluidized bed were compared at different flow rates (U_g) to conventional flat‐wall fluidized bed using high‐speed digital image analysis. Hydrodynamic studies were carried out to appraise the effect of triangular‐shaped wall corrugation on incipient fluidization, bubble coalescence (size and frequency), bubble rise velocity, and pressure drop. Bubble size and rise velocity in corrugated‐wall beds were appreciably lower, at given U_g/U_mb, than in flat‐wall beds with equal flow cross‐sectional areas and initial bed heights. The decrease (increase) in size (frequency) of bubbles during their rise was sustained by their periodic breakups while protruding through the necks between corrugated plates. Euler‐Euler transient full three‐dimensional computational fluid dynamic simulations helped shape an understanding of the impact of corrugation geometry on lowering the minimum bubbling fluidization and improving gas distribution. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Capillary flow of low‐density polyethylene

The capillary flow of a commercial low‐density polyethylene (LDPE) melt was studied both experimentally and numerically. The excess pressure drop due to entry (Bagley correction), the compressibility, the effect of pressure on viscosity, and the possible slip effects on the capillary data analysis have been examined. Using a series of capillary dies having different diameters, D, and length‐to‐diameter L/D ratios, a full rheological characterization has been carried out, and the experimental data have been fitted both with a viscous model (Carreau‐Yasuda) and a viscoelastic one (the Kaye—Bernstein, Kearsley, Zapas/Papanastasiou, Scriven, Macosko, or K‐BKZ/PSM model). Particular emphasis has been given on the pressure‐dependence of viscosity, with a pressure‐dependent coefficient β_p. For the viscous model, the viscosity is a function of both temperature and pressure. For the viscoelastic K‐BKZ model, the time‐temperature shifting concept has been used for the non‐isothermal calculations, while the time–pressure shifting concept has been used to shift the relaxation moduli for the pressure‐dependence effect. It was found that only the viscoelastic simulations were capable of reproducing the experimental data well, while any viscous modeling always underestimates the pressures, especially at the higher apparent shear rates and L/D ratios. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

Homogenized tensile and bending properties of plain weave single‐Ply E‐glass/epoxy

This study empirically, numerically, and analytically analyzes the tensile and bending behavior of a plain weave single‐ply E‐glass/epoxy composite. In the empirical part of the study, tensile and simple bending experiments are conducted. Finite element method is used in the modeling part of the numerical study. Transverse and longitudinal fibers of the plain woven composite are modeled in one and three dimensions by using the ABAQUS software. Finally, mixture ratio approach and composite beam approach are considered in the analytical part of the study. Elastic modulus, Poisson's ratio, bending stiffness, and critical bending radius are obtained experimentally and are compared with the results of the finite element analyses and the results of the analytical study where applicable. The results closest to the empirically obtained ones are obtained by three‐dimensional (3D) finite elements analysis. Moreover, the mechanical characteristics obtained by the composite beam approach used in the analytical study are also very close to the values obtained by 3D finite elements analysis. POLYM. COMPOS., 2012. © 2012 Society of Plastics Engineers     

Investigation of combination of finite element formulation and element type on the accuracy of 3D modeling of polymeric fluid flow in an extrusion die

The aim of this work is to investigate the effect of finite element formulation and element type on the accuracy of 3D modeling of generalized Newtonian fluid flow in complex domains. Computer models based on three finite element solution schemes (mixed, continuous, and discrete penalty), and two element types (hexahedral and tetrahedral) in a 3D framework were developed. The well‐known Carreau model was used to reflect the rheological behavior of the fluid. To determine the validity of the developed computer simulations, the flow of two high‐density polyethylene (HDPE) melts with different viscosities through an extrusion die was simulated and compared with experimentally measured data. Comparison showed that the three methods produced nearly the same results with the hexahedral elements. However, continuous penalty method using tetrahedral elements demonstrated an extreme discrepancy from the experimental data. Discrete penalty method was unable to predict secondary variable (pressure) accurately using tetrahedral elements. The best results were obtained by the use of mixed method in conjunction with tetrahedral elements. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Optimization analysis of the staggered herringbone micromixer based on the slip-driven method

In this paper the mixing effect of the staggered herringbone micromixer (SHM) was investigated by using the slip-driven method. This method simplified the 3D flow in the staggered herringbone micromixer into a 2D cavity flow with an axial Poiseuille flow. The solution of the 2D cavity flow was obtained by solving the biharmonic equation. An improved design with a cosine asymmetric factor P(z) was proposed, and its mixing effect was demonstrated by comparing the effect with the original design [Stroock, A.D., Dertinger, S.K.W., Ajdari, A., Mezic, I., Stone, H.A. and Whitesides, G.M., 2002, Chaotic mixer for microchannels, Science, 295: 647–651; Stroock, A.D., Dertinger, S.K.W., Whitesides, G.M. and Ajdari, A., 2002, Patterning flows using grooved surfaces, Anal Chem, 74: 5306–5312]. Four methods evaluating the mixing effect were used: (1) mixing images at different cycles; (2) Poincaré Sections; (3) segregation intensity and (4) stretching computation. Finally, an optimized value of P₀ = 1/6 was obtained, and the mixing effect of the improved design for different P₀ is discussed.     

Numerical and experimental study on spout elevation in spout‐fluidized beds

The effect of elevating the spout on the dynamics of a spout‐fluidized bed, both numerically and experimentally is studied. The experiments were conducted in a pseudo‐two‐dimensional (2‐D) and a cylindrical three dimensional (3‐D) spout‐fluidized bed, where positron emission particle tracking (PEPT) and particle image velocimetry (PIV) were applied to the pseudo‐2‐D bed, and PEPT and electrical capacitance tomography (ECT) to the cylindrical 3‐D bed. A discrete particle model (DPM) was used to perform full 3‐D simulations of the bed dynamics. Several cases were studied, that is, beds with spout heights of 0, 2, and 4 cm. In the pseudo‐2‐D bed, the spout‐fluidization and jet‐in‐fluidized‐bed regime, were considered first, and it was shown that in the spout–fluidization regime, the expected dead zones appear in the annulus near the bottom of the bed as the spout is elevated. However, in the jet‐in‐fluidized‐bed regime, the circulation pattern of the particles is affected, without the development of stagnant zones. The jet‐in‐fluidized‐bed regime was further investigated, and additionally the experimental results obtained with PIV and PEPT were compared with the DPM simulation results. The experimental results obtained with PIV and PEPT agreed mutually very well, and in addition agreed well wtih the DPM results, although the velocities in the annulus region were slightly over predicted. The latter is probably due to the particle‐wall effects that are more dominant in pseudo‐2‐D systems compared with 3‐D systems. In the jet‐in‐fluidized‐bed regime, the background gas velocity is relatively high, producing bubbles in the annulus that interact with the spout channel. In the case of a non elevated spout, this interaction occurs near the bottom of the bed. As the spout is elevated, this interaction is shifted upwards in the bed, which allows the bubbles to remain undisturbed providing the motion of the particles in the annulus near the bottom of the bed. As a result, no dead zones are created and additionally, circulation patterns are vertically stretched. These findings were also obtained for the cylindrical 3‐D bed; although, the effects were less pronounced. In the cylindrical 3‐D bed the PEPT results show that the effect on the bed dynamics starts at h_spout =1 4 cm, which is confirmed by the ECT results. Additionally, ECT measurements were conducted for h_spout =1 6 cm to verify if indeed the effect happens at larger spout heights. The root mean square of the particle volume fraction slightly increased at h_spout =1 2 cm, whereas a larger increase is found at h_spout = 4 and 6 cm, showing that indeed more bubbles are formed. The presented results have not been reported so far and form valuable input information for improving industrial granulators. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2524–2535, 2012     

Rheological behaviors of glass bead‐ and wollastonite‐filled polypropylene composites modified with thermoplastic elastomers

Steady‐ and oscillatory‐shear rheological behaviors of polypropylene/glass bead (PP/GB) and PP/wollastonite (PP/W) melts modified with thermoplastic elastomers, poly(styrene‐b‐ethylene‐co‐butylene‐b‐styrene) copolymer (SEBS) and the corresponding block copolymer grafted with maleic anhydride (SEBS‐g‐MA), were examined by means of a parallel‐plate rheometer. With adding the elastomers (SEBS and SEBS‐g‐MA) and fillers (spherical GB and acicular W) to PP, viscosity especially at low shear rates and shear‐thinning flow behavior at high shear rates were pronounced as evidenced quantitatively by Carreau–Yasuda (CY) parameters, but Cox–Merz analogy became weakened. Besides, melt‐elasticity in terminal region and relaxation time (t_c) in crossing point increased, indicating an enhancement in quasi‐solid behavior of molten PP. Comparing with the elastomers, rheological behaviors of molten PP were more influenced with adding the rigid fillers, especially with W due to distinct acicular shape of W particles. SEBS‐g‐MA elastomer more affected rheological behaviors of the ternary composites than SEBS elastomer, implying that SEBS elastomer and the filler particles behaved individually (i.e., development of separate microstructure) in (PP/GB)/SEBS and (PP/W)/SEBS ternary composites, but core‐shell microstructure developed with strong interfacial adhesion by adding SEBS‐g‐MA elastomer, and the filler particles encapsulated with the thick SEBS‐g‐MA elastomer interlayer (i.e., core‐shell particles) acted like neither big elastomer particles nor like individual rigid particles in melt‐state. Moreover, effects of SEBS‐g‐MA elastomer reached a maximum on rheological behaviors of (PP/W)/SEBS‐g‐MA ternary composite, indicating a synergy between core‐shell microstructure and acicular W particles. Correlations between oscillatory‐shear flow properties and microstructures of the blends and composites were evaluated using Cole–Cole (CC), Han–Chuang (HC), and van Gurp–Palmen (vGP) plots. COMPOS., 2012. © 2012 Society of Plastics     

Polymeric superabsorbing composite prepared using a glow‐discharge electrolysis plasma for the removal of divalent heavy metal ions from aqueous solutions and its swelling properties

A novel polymeric superabsorbing composite was prepared using the graft copolymerization of acrylic acid (AANa, 70% neutralization with NaOH) and 2‐acrylamido‐2‐methyl propane sulfonic acid (AMPS) onto the hydroxyethyl cellulose (HEC) [HEC‐g‐P(AANa‐co‐AMPS)], which was initiated by means of a glow‐discharge electrolysis plasma rather than a chemical initiator. The composite material was characterized by Fourier transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), and thermal gravimetric analysis (TGA). We obtained absorbencies of 2490 g g^?1 for distilled water and of 109 g g^?1 for 0.9 wt% NaCl solution. Results show that the maximum adsorption capacities for Ni(II), Cu(II), Cd(II), Pb(II), and Hg(II) from aqueous solution were 974.84, 975.43, 1535.52, 1970.47, and 1879.53 mg g^?1, respectively. The adsorption isotherm followed the Langmuir isotherm model very well. Adsorption kinetics results indicate that the fast adsorption rate followed the pseudo‐second‐order kinetics equations. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

Preparation and characterization of microbial biodegradable poly(3‐hydroxybutyrate‐co‐4‐hydroxybutyrate)/organoclay nanocomposites

Novel biodegradable poly(3‐hydroxybutyrate‐co‐4‐hydroxybutyrate) [P(3HB‐co‐4HB)]/organoclay nanocomposites were prepared via solution casting. Exfoliated nanocomposite structure was confirmed by wide‐angle X‐ray diffraction (WAXD) and transmission electron microscopy (TEM) for the nanocomposites with low organoclay loadings (≤3 wt%), whereas the mixtures of exfoliated and unexfoliated organoclays were appeared in the nanocomposite with an organoclay content of 5 wt%. The organoclay fillers accelerated significantly the cold crystallization process of P(3HB‐co‐4HB) matrix. The thermal stability of the nanocomposites was in general better than that of pristine P(3HB‐co‐4HB). Considerable increase in tensile modulus was observed for the nanocomposites, especially at an organoclay content of 3 wt%. These results demonstrated that the nanocomposites improved the material properties of P(3HB‐co‐4HB). POLYM. COMPOS., 2012. © 2012 Society of Plastics Engineers     

Permeability mapping in naturally heterogeneous sandstone cores by magnetization prepared centric‐scan sprite

A time‐efficient MRI method suitable for quantitative two‐dimensional (2‐D) mapping of permeability in sedimentary rock cores, and granular media samples is discussed. The images of porosity and mean axial velocity in the plane transverse to the average flow direction are essential to determine 2‐D distribution of permeability in a core sample. The 2‐D permeability mapping is particularly useful for discrimination of bedding and lamination layers, fractures and fault facies that occur in sedimentary rocks. The proposed method combines the 13‐interval APGSTE scheme and centric‐scan SPRITE. The APGSTE scheme is known to substantially reduce gradient‐related errors in diffusion measurements. The SPRITE method provides quantitative information on fluid content within the core samples. The experiment time is critically reduced when only a few samples near the q‐space origin are collected. The APGSTE‐SPRITE method is illustrated through mapping of 2‐D permeability and 3‐D velocity field in naturally heterogeneous sandstone cores. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Analysis of a liquid‐assisted molding process for coating microchannels with an ultraviolet curable polymer

Injection molding can be altered to form hollow parts by partially pre‐filling a mold with polymer melt and then injecting a gas into the mold before cooling. The gas will core the center section and in the process force melt into the unfilled portions of the mold. This process is called gas‐assisted injection molding (GAIM) and is a thoroughly studied polymer processing technique. Liquid‐assisted molding follows the same principles as GAIM, except the coring fluid is a liquid of low viscosity. Liquid‐assisted molding of an ultraviolet (UV) curable polymer can be used to coat microchannels, the benefit of which being a smooth and circular cross‐section. Presented here are experiments of the controlled microchannel flow of a long, immiscible liquid thread through a viscous UV curable polymer. The roles of channel geometry and bubble velocity are discussed for square, rectangular, and circular microchannels. Finally, a quasi‐analytical model for calculating the Newtonian coating fluid thickness, when the coring fluid is driven by a constant pressure, was developed using the equation for Poiseuille‐like flow within a square channel. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

Numerical simulation of thickness variation effect on resin transfer molding process

In this work, a computer model has been developed to investigate the effect of reinforcement thickness variation and edge effect on infiltration and mold filling in resin transfer molding (RTM) process. The developed code is able to predict the flow front location of the resin, the pressure, and the temperature distribution at each time step in a mold with complex geometries. It can also optimize the positioning of injection ports and vents. The filling stage is simulated in a full two‐dimensional space by using control volume/finite element method CV/FEM and based upon an appropriate filling algorithm. Results show that the injection time as well as flow front progression depends on the edge effect, the variation of reinforcement thickness, and the position of injection ports; this highlights that the inclusion of these effects in RTM simulation is of definite need for the better prediction and optimization of the process parameters. The validity of our developed model is evaluated in comparison with analytical solutions for simple geometries, and excellent agreements are observed. POLYM. COMPOS., 2012. © 2011 Society of Plastics Engineers