Numerical Simulation of Extrusion Characteristics for Co-rotating Tri-Screw Extruder

The flow of polyethylene melt in new tri-screw extruder was simulated using the finite element method (FEM). A special study of flow in central region was performed by analysis of the velocity, pressure, and resident time distribution (RTD). The extrusion characteristics of tri-screw extruder, namely the abilities of material conveying, mixing, and power consumption, were compared with those of twin screw extruder. The results showed that there was circumfluence in central region but no stagnation in it. Tri-screw extruder had better operative abilities and high productivity ratio than twin screw extruder in the aspect of material conveying and mixing.     

Finite element analysis of flow of thermoplastic elastomer melt through axisymmetric die with slip boundary condition

Abstract

A finite element model for the flow of thermoplastic elastomers in extrusion dies has been developed. The rheological behaviour of the polymer melt is assumed to be described by the generalised Newtonian models and as a special case, the well known, power law equation was selected. Owing to the very low variation of the temperature field, the flow regime was considered to be isothermal. The set of governing equations are solved using the finite element method in a cylindrical (r, z) coordinate system. Slip–stick of the polymer melt on the solid wall, encountered in the flow of highly viscous fluids, is incorporated into the model by the use of Navier's slip condition. A new method based on a technique developed previously is described for the inclusion of this condition in the working equations. The applicability of the model was verified by a comparison between the results of the simulation of a polypropylene–nitrile/butadiene rubber thermoplastic elastomer with experimentally measured data. These comparisons show that there are very good agreements between the model predictions and actual data, provided that the slip of the polymer melt during the flow in extrusion die has been taken into consideration.     

MATHEMATICAL SIMULATION OF TEMPERATURE AND MOISTURE FIELDS WITHIN A GRAIN KERNEL DURING DRYING

ABSTRACT

Non-linear partial differential equations are presented for two dimensional heat and mass transfer within a single grain kernel during drying. In this model, the moisture evaporation inside the kernel is considered. The moisture is assumed to diffuse to the outer boundary of the kernel in liquid form and evaporate on the surface of the kernel. The influence of temperature and moisture content on grain properties is also considered in the simulation. The Non-linear partial differential equations are solved using the finite element method and simulation data is verified on a thin layer dryer for wheat kernels. The comparison shows that the simulated results have a high accuracy with average relative error of about 5%. The results of the finite element analysis can be used for grain quality evaluation, drying simulation studies and stress analysis of grain kernel.     

Effect of the axial vibration of screw on residence time distribution in single‐screw extruders

An analytic model has been developed to analyze the residence time distribution of melt in the screw channel of the melt conveying section in a novel extruder of which the screw can vibrate axially. A comparison of the residence time distribution of melt in screw channel with and without vibration shows that the residence time of melt increases with the apply of vibration and the larger the vibration frequency and amplitude are, the longer time it will take the melt to travel through the melt conveying section, which is in favor of the improvement of the effect of melt mixing. POLYM. ENG. SCI. 46:198–204, 2006. © 2005 Society of Plastics Engineers     

PSEUDO TWO-DIMENSIONAL MODEL FOR A PNEUMATIC DRYER

ABSTRACT

Pneumatic drying of chemical products has been frequently used in chemical industries. The increase in the use of this unit operation requires the knowledge of the dynamic of the gas-solid flow in tubes. The mathematical models of vertical pneumatic conveying found in the literature mostly consider the flow steady and one dimensional. However, experimental evidences suggest that radial profiles of the basic variables of the flow exist. In this work a model is proposed for vertical pneumatic conveying considering axial and radial profiles for gas and solids velocities, porosity and pressure. The conservation equations for energy and mass of water were written to extend the model to a pneumatic dryer. The equations of the model were solved using finite difference method and the results show the axial and radial variations of gas and solid temperatures, gas humidity and particle moisture content in the dryer.     

啮合同向三螺杆挤出机中三维等温流动的数值模拟

Three-dimensional isothermal flow of polymer melt in the kneading-disc element of an intermeshing co-rotating tri-screw extruder was simulated by using finite element package POLYFLOW. Based on the velocity fields calculated, flow patterns of the melt were analyzed, and particle trajectories were visualized. The numerical results indicated that, in intermeshing co-rotating tri-screw extruders, particles went through three intermeshing regions during one cycle around the screws, thus achieving better plasticating and mixing than intermeshing co-rotating twin-screw extruders. Flow in the central region was also studied by using particle tracking technique, and residence time distribution (RTD) and trajectories for particles in this region were presented. The simulation results showed that there was no stagnation in the central region. This study provided a clear insight into the flow mechanism of tri-screw extrusion. It also provided a new method for studies of flow mechanisms in other complicated mixers.     

a rview of: UNIFIED ANALYSIS AND SOLUTIONS OF HEAT AND MASS DIFFUSION

ABSTRACT

The objective of this study is the formulation of a finite element model that could be used to analyze the stress crack formation in a viscoelastic sphere resulting from temperature and moisture gradients during the drying process. Numerical solutions to the simultaneous moisture and heat diffusion equations describing moisture removal and heat intake process for the sphere are obtained. The distribution and gradients of temperature and moisture developed inside the sphere during drying are established. The calculated temperature and moisture gradients are used in a finite element analysis of the thermo-hydro viscoelastic boundary value problem to simulate the stresses in the body.

The model is used to solve a sample problem of drying a soybean kernel. The simulated drying curve for the soybean model is obtained and compared favorably with the experimental results reported in the literature. Tangential stress, as a criteria for failure, is shown to change from compressive to tensile stress as it approaches the surface. It reaches its peak value at the surface in one hour and then decays slowly. The effect of different drying conditions is studied and the results are discussed.     

A 2-d numerical study of intermeshing self-wiping screws in biopolymer extrusion

A knowledge of flow behavior is important in the study of laminar flow in twin-screw extrusion processes to predict the velocity distribution and to understand the mixing process. The flow of a power law fluid in self-wiping twin-screw extruders is examined using a two-dimensional finite element analysis of a mid-channel section of intermeshing screws. Theory is compared with experiment using food biopolymer and plastic materials. Comparisons showing overprediction of throughputs, but similarities in behavior, suggest that this model could provide an upper limit for melt conveying. For most of the throughput range examined, pumping of intermeshing self-wiping screws appears to be almost independent of the power law flow index of the melt extruded, but the value of the flow index determines the degree of influence intermeshing has on the overall pressure gradient generated in the extruder.     

Effect of Pressure on Moisture Transfer During Moisture Adsorption

ABSTRACT

A set of coupled heat, mass, and pressure transfer equations was used to describe the moisture adsorption process in gmn kernels. The finite element method was used to solve the system of equations. The technique was applied to analyze the temperature, moisture, and pressure distribution in a barley kernel during soaking with steep water. The temperature and moisture distributions with (heat, mass, and pressure transfer model) and without (heat and mass uansfer) the effect of pressure were simulated for assumed conditions. The results obtained from the heat, mass, and pressure transfer model show a marked difference from the results obtained from the heat and mass transfer model. This indicated that a pressure gradient exists during the transfer Process, causing additional moisture movement due to filtration effect. Hence. the pressure tern cannot be assumed constant during the moisture adsorption process. The simulated temperature, moisture and pressure profiles and gradients can be used for determining the optimum time required for solking kernels with sleep water to produce barley malt.     

Modeling of single-screw extruders with mixing pins: The case of PVC

A computer model is proposed to simulate the flow of molten polymer in the melt conveying zone of extruders provided with mixing pins. This model is based on the calculation of down-channel velocities within cross sections perpendicular to the flow. A Lagrangian reference frame (i.e. that of the barrel sliding on top of the channel) is used to describe the flow in a convenient manner, the mixing pins being represented as a set of virtual boundary conditions (geometric constraints). The proposed method is compared to a full 3D finite element flow simulation with Newtonian and non-Newtonian fluids showing a good agreement in term of the pressure drop calculation. Numerical tests are also carried out in the case of a rigid PVC compound used for window profile extrusion. The adequacy found between the predictions and experimental measurements obtained on an industrial extruder confirms the performance of the proposed model.     

MODELING VACUUM-CONTACT DRYING OF WOOD: THE WATER POTENTIAL APPROACH

ABSTRACT

A two-dimensional mathematical model for vacuum-contact drying of wood is presented. The moisture and heat equations are based on the water potential concept whereas the pressure equation is formulated considering unsteady state conservation equation of dry air. Most of the model parameters were determined during independent experiments. The set of equations is then solved in a coupled form using the finite element method. The validation of the model is performed using experimental results obtained during vacuum-contact drying of sugar maple sapwood. The experimental and calculated data are in good agreement. Nevertheless, some discrepancies are observed which can be attributed to the boundary conditions used and to the fact that heat transfer by convection was neglected.     

A numerical model for single screw extrusion with poly(vinyl chloride) (PVC) resins

A computer model has been developed to simulate the behavior of molten polymer in the melt conveying zone of extruders. This model, based on a hybrid finite difference/finite element resolution of the equations of change governing momentum and heat transfer, allows the prediction of the pressure profile while accounting for wall end effects as well as the solid bed velocity. Simulation results are compared with analytical and finite difference method results found in the literature. A fairly good agreement is obtained in the case of low density polyethylene. Numerical tests are also carried out with rigid poly(vinyl chloride) compound used for window profile extrusion. The good agreement found between the predictions and experimental measurements obtained on an industrial extruder confirms the performance of the proposed model.     

Unsteady-State Model for Continuous Moving-Bed Chromatography

Abstract

Mathematical equations have been formulated to predict the longitudinal concentration distribution in the case of instantaneous behavior of a continuous chromatographic system. Partial differential equations are initially obtained from mass balance on the differential element of column height. The formulated equations are solved by Lap lace transformation and the contour integration method. Two equations are obtained, one for the column section above the feed point and the second for the column section below the feed. Both of these equations give the concentration distribution along the appropriate section of the column. The model predicts the instantaneous and steady-state behavior of the continuous moving-bed chromatographic system. The model can also be used as a tool for the design of new continuous chromatographic columns.     

自然对流对于熔体生长中小面化的影响

应用基于边界保角变换技术的Ｇａｌｅｒｋｉｎ有限元方法，研究熔体生长中动力学效应和自然对流的耦合作用探究了对流对生长系统中的温场分布、相界面２以及界面过冷度的影响。研究结果表明：自然对不充可使相界面的弯曲度减小，界面的相对位置降低，同时，对流使得小面端点处的夹角变得圆滑，小面域和粗糙面域的界线变得不明显，相应地，小面尺寸有所减小。     

DETERMINATION OF MASS DIFFUSIVITY COEFFICIENT OF SWEET POTATO

Abstract

Using Luikov's heat and mass transfer equations and a finite element formulation, the drying process of an anisotropic biological product (sweet potato) was investigated. The model was used to determine the coefficients of heat and mass transfer, the mass diffusivity normal and parallel to the fibers of sweet potato samples. These parameters were estimated by minimizing the deviation of experimental data and numerical predictions.

Laboratory experiments with three different configurations were conducted to measure the temperature and moisture content of sweet potato samples during drying. Numerical simulation showed good agreement with the measured values.     

振动力场作用下聚合物熔体单螺杆挤出过程数值模拟

根据塑料电磁动态塑化挤出过程中熔体输送的实际情况，对三维模型进行简化，利用大型有限元软件ANSYS模拟了叠加轴向振动力场作用下聚合物熔体在螺槽中的流动情况，求解出周期性变化的速度，压力场分布，结果表明，与稳态挤出过程相比，振动力场的引入在进出口压力差恒定的情况下，可以提高熔全输送流率。采用有限元模拟方法可以为确定和优化工艺参数，产品质量控制提供指导。     

Methodology to evaluate variations in piezoelectric constants after aging process

ABSTRACT

Piezoelectric ceramic properties change with time. Detected aging effects for PZT ceramics are; the difference in the value of the dielectric constants diminishes, whereas dielectric losses and elastic stiffness increases. In this work, an optimisation technique based on adjusting a finite element model to reproduce the complex impedance curves of a resonant piezoceramic disk is analysed aiming to detect changes due to aging. This technique allows estimating all material parameters, both their real and imaginary parts. The optimisation uses the constitutive equations of the piezoelectric effect in the linear regime. The evolution of elastic, piezoelectric and dielectric constants is evaluated after 5 years of aging. To compute the ten complex parameters, the piezoelectric model is adjusted to minimise the difference between finite element simulations and the experimental data. Results presented here, show that the proposed technique is sensitive enough to detect changes in the individual parameters due to aging process.     

Improving mixing characteristics with a pitched tip in kneading elements in twin‐screw extrusion

In twin‐screw extrusion, the geometry of a mixing element mainly determines the basic flow pattern, which eventually affects the mixing ability as well as the dispersive ability of the mixing element. The effects of geometrical modification, with both forward and backward pitched tips, of a conventional forward kneading disks element (FKD) in the pitched‐tip kneading disks element on the flow pattern and mixing characteristics are discussed. Numerical simulations of fully filled, nonisothermal polymer melt flow in the melt‐mixing zone were performed, and the flow pattern structure and the tracer trajectories were investigated. The pitched tips largely affect the inter‐disk fluid transport, which is mainly responsible for mixing. These changes in the local flow pattern are analyzed by the distribution of the strain‐rate state. The distribution of the finite‐time Lyapunov exponent reveals a large inhomogeneity of the mixing in FKD is suppressed both by the forward and backward tips. By the forward tips on FKD, the mixing ability is relatively suppressed compared to FKD, whereas for the backward tips on FKD, the mixing ability is enhanced while maintaining the same level of dispersion efficiency as FKD. From these results, the pitched tips on the conventional KD turn out to be effective at reducing the inhomogeneity of the mixing and tuning the overall mixing performance. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1424–1434, 2018     

Flow and mixing efficiency characterisation in a CO2-assisted single-screw extrusion process by residence time distribution using Raman spectroscopy

Hot-melt extrusion of a bio-sourced polyamide has been implemented in a single-screw extruder with supercritical carbon dioxide injection. CO₂ acts as a plasticiser in the extruder barrel and as a physical blowing agent at the die. To insure a better mixing and dissolution of the CO₂ into the polymer melt, addition of a static mixer between the screw tip and the die was tested. The effect of both the static mixing element and the CO₂ injection on the melt flow behaviour has been elucidated. A recent technique of in-line Raman spectroscopy was implemented to make a residence time distribution study, using titanium dioxide as a tracer. The use of a static mixer exerts a major modification on the flow behaviour: it improves mixing by enhancing dispersion. In addition, the structure of the manufactured products was studied: the static mixer led to more homogeneous porous structure. The broad range of CO₂ incorporation (up to 25%, w/w) into the melt led to the manufacture of foams with adjustable porosity from 15 to 70%.     

Evaluation of experimental techniques to validate numerical computations of the hydraulics inside a UV bench-scale reactor

Computational fluid dynamics (CFD) is widely used to predict the hydraulics in environmental systems, but the validity of these predictions continues to receive attention. The hydraulics of a UV bench-scale reactor was evaluated by numerical and experimental techniques. Different experimental techniques were used to examine the hydraulics: salt injection to measure the residence time distribution, dye injection to visualize the mixing patterns, and LDA to measure the local velocity profiles. The combination of these measurements techniques provides information in unprecedented detail of the hydraulics inside UV systems. A CFD model with a standard k?ε turbulence model was used for comparison with the experimental results. The main flow patterns were predicted well. The largest differences were found at regions in the reactor where recirculation occurred, for example in the wake region of a lamp. Also, the CFD model predicted a larger mixing over the flow cross-section, resulting in a narrower residence time distribution.