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.     

AN EXPERIMENTAL AND NUMERICAL INVESTIGATION OF TURBULENT RECIRCULATING FLOW IN A CAVITY WITH AN INLET WALL JET

Recirculating turbulent flow within a cavity with an inlet wall jet was examined. In steady water flow profiles were constructed with measurements taken with a Laser Dopplcr Anemometer system mounted on a traversing mechanism for two different inlet velocities. The results are presented in terms of mean velocities and turbulent kinetic energy distributions. Comparisons are then made with results obtained using a finite difference computational scheme based on the k-ε turbulence model. In general, good agreement was obtained between the computer code predictions and the experimental data. However, the agreement between measurements and the code predictions was much better for the mean velocity field as compared to the turbulent kinetic energy field.     

Material and finite element analysis of poly(tetrafluoroethylene) rotary seals

Abstract

The stress-strain characteristics of PTFE under uniaxial tension and compression have been measured at various temperatures. A new finite element analysis procedure using MARC is presented, which can simulate the different properties of PTFE from tension and compression data. This method is based on using the maximum principal stress value at the integration point of each element to define whether the element is under tension or compression at each increment, then using subroutines to specify the material properties. A positive value indicates a state of tension and a negative value indicates compression. It has been found that the finite element analysis results are in good agreement with those from experiment. Finally, a PTFE rotary seal was modelled using this new method, and results were obtained incorporating stress and lip loads of the rotary seal, with different temperature effects.     

Fast Prediction Method for Steady‐State Heat Convection

A reduced model by proper orthogonal decomposition (POD) and Galerkin projection methods for steady‐state heat convection is established on a nonuniform grid. It was verified by thousands of examples that the results are in good agreement with the results obtained from the finite volume method. This model can also predict the cases where model parameters far exceed the sample scope. Moreover, the calculation time needed by the model is much shorter than that needed for the finite volume method. Thus, the nonuniform POD‐Galerkin projection method exhibits high accuracy, good suitability, and fast computation. It has universal significance for accurate and fast prediction. Also, the methodology can be applied to more complex modeling in chemical engineering and technology, such as reaction and turbulence.     

FEM calculations of capillary rheometer flow for carbon‐filled liquid crystal polymer composites

There is an emerging market for conductive resins for use in fuel cell bipolar plates. This research focuses on developing a finite element model of a capillary rheometer. Comsol Multiphysics 3.2b was used to model the flow of a remeltable thermoplastic matrix material, Vectra A950RX Liquid Crystal Polymer, with varying amounts of either a carbon black or synthetic graphite filler, to obtain the velocity profile and pressure drop of these composites within the capillary. Previous experimental results have shown that the molten composites obey a shear‐thinning power law behavior. When comparing the model predicted pressure drops from the model with the experimental data, very good agreement was obtained. This signifies that the rheological behavior of the composites can be described by a power law relationship, using parameters specific to each composite. When comparing the modeled velocity profile with the theoretical profile, it was found for all composite formulations that the velocity becomes fully developed within a length of 0.05 times the diameter of the tube, independent of the power law parameters n and m. This work is a necessary first step in developing 2D or 3D mold filling simulations for fuel cell bipolar plate applications. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

Two-fluid modelling of the rewetting and refilling of hot horizontal tubes

This paper deals with the use of a two-fluid model for predicting the thermal-hydraulic characteristics of the rewetting and refilling of hot horizontal tubes. The two-fluid model equations were simplified and solved using an explicit finite difference scheme. A set of constitutive equations is used for closure. A new film boiling model and a model for evaluating the rate of latent to total heat in film boiling were incorporated in the two-fluid model. A newly proposed rewetting criterion, based on vapour film collapse, was used to mark the end of the film boiling regime. The model is capable of predicting the rewetting and refilling process in horizontal tubes under conditions of stratified or inverted annular refilling flow. The model predictions were found to be in good agreement with the experimental results.     

Calibration of dielectric constant measurements to improve the detection of cloud and clear points in solution crystallization

Metastable zone width, which can be approximated as the gap between the loci of cloud and clear points is an important control parameter for successful operations of solution crystallization processes. This study attempts to improve the accuracy of cloud point determination in paracetamol-ethanol solution using dielectric constant measurements and a special calibration technique. A suitable calibration model based on logarithm-polynomial expansion is developed using adjusted R² and Akaike Information Criterion as model selection guides. The model, which decouples the effects of temperature and solute concentration on solution dielectric constant, is utilized to transform the dielectric constant profile into a solute concentration profile. The results show that the cloud points determined from the solute concentration profile are more accurate than those determined directly from the dielectric constant profile. The former are shown to be in good agreement with those obtained from the turbidity measurements, which are used as benchmarks in this study. Consequently, a more accurate metastable zone width could also be obtained using this calibration technique.     

Release of ibuprofen from poly(ε‐caprolactone‐co‐D,L‐lactide) and simulation of the release

A study was made of the effects of the initial ibuprofen load and of the specimen shape on the release of ibuprofen from poly(ε‐caprolactone‐co‐D,L ‐lactide). The mol ratio of the comonomers in the copolymer was 96/4 (caprolactone to lactide) and the experiments were conducted at 37°C in vitro. The results showed that release of ibuprofen is fast and that the rate and profile of the release vary with both the initial load of ibuprofen and the shape of the specimen. The rate of ibuprofen release increases with the initial load and with the surface area‐to‐volume ratio of the specimen, obeying Fickian diffusion. The experimental findings were compared with the results of a mathematical simulation model based on the finite‐difference method. Diffusion parameters needed for the simulation were determined from a separately conducted set of experiments using various methods. For the most part, the results of the simulations and the experiments were in good agreement. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 1279–1288, 2003     

Simulation of residual stress in thick thermal barrier coating (TTBC) during thermal shock: A response surface-finite element modeling

The current study demonstrates a well-designed response surface methodology (RSM), based on the generated dataset of finite element method (FEM) to establish an integrated model for simulation of residual stress distribution in a thick thermal barrier coating (TTBC). In this study, typical TTBCs were applied on Hastelloy X Nickel-based superalloy using air plasma spray technique followed by thermal cycling. The recorded stress data of Raman spectroscopy was employed to verify the proposed FEM model. A relatively good agreement was obtained between predicted residual stresses and measured ones. Verified FEM model was used to carry out the parametric studies to evaluate the effects of such various parameters as interface amplitude, wavelength, thermally grown oxide thickness and preheating temperature on the stress distribution in the TTBC during the thermal cycling. The computed data were subsequently used for the development of RSM model. In conclusion, experimentally verified numerical data was used to construct a statistical model based on RSM and successfully used to predict the residual stress distribution field in TTBC during thermal cycling. The obtained results of hybrid FEM- RSM model were in acceptable conformity with Raman spectroscopy measurements.     

Three‐dimensional simulation of microchip encapsulation process

A finite element simulation of moving boundaries in a three‐dimensional inertiafree, incompressible flow is presented. A control volume scheme with a fixed finite element mesh is employed to predict fluid front advancement. Fluid front advancement and pressure variation in a flow domain similar to the mold cavity used for microchip encapsulation are predicted. The predicted fluid front advancement and pressure variation are in good agreement with the corresponding experimental results. As the difference in the thicknesses of mold cavities above and below the microchip is changed, the weld line location and pressure variation during mold filling are found to change significantly.     

CFD simulation of the hydrodynamics and reactions in an activated sludge channel reactor of wastewater treatment

This paper presents a complete CFD modelling of a wastewater gas-liquid cross-flow reactor, taking into account hydrodynamics, mass transfer and biological reactions. Transfer processes, kinetics model and assumptions made are described in detail. The simulations have been successfully compared to experimental results obtained in a bench scale reactor. Chemical oxygen demand (COD), nitrate, ammonium and oxygen concentrations have been measured along the length of the reactor and compared to the simulated profiles. A very good agreement has been obtained for the COD and nitrate concentration profiles. Agreement for the oxygen concentration profile is reasonably good with respect to the experimental uncertainty. These results have been obtained without any adjustment of the kinetics parameters. The basics of a three-phase CFD model taking into account the transfer between flocs and wastewater, as well as the inhomogeneous concentration of biomass due to the hydrodynamics of the reactor, are proposed as perspectives.     

Distribution of the thermal residual stresses in the WC-Co microstructure by finite element method

A Finite Element Model is used to observe the build-up of residual thermal stresses during the sintering process in two WC-Co samples with different volume fractions of Co. A realistic model of the two phase material is obtained by FIB slicing a real WC-Co sample and reconstituting the morphology. In the finite element model, the WC phase is defined as elastic and the Co phase includes plasticity. Different sets of parameters are considered to model the two phases. The results are compared with experimental data obtained by neutron diffraction. A good agreement is obtained between the experimental data and the simulations. The spatial distribution of the stress in the WC phase is also observed. This observation reveals anisotropy in the microscopic behavior, with the presence of preferential directions for the build-up of stress.     

Effect of Surfactant Concentration on the Dispersion Coefficient for the Comparison of Model and Experimental Results in Emulsion Polymerization of Butadiene

In this work, a mechanistic model was developed on the basis of population balance equations for butadiene emulsion polymerization and validated with experimental data in a batch reactor. A combination of finite difference and weighted essentially nonconciliatory (WENO) schemes was used as a precise technique for the discretization of the population balance equations. The obtained values during the evolution of conversion and the average particle diameter values were in good agreement with the measured results for different surfactant concentrations. However, the simulated particle-size distributions (PSDs) were much narrower than the experimental PSDs. Therefore, to match the experimental PSDs, a stochastic term was included in the zero–one model. The effect of surfactant concentration, which is an important factor with a direct impact on the dispersion coefficient, was also investigated and confirmed with experimental results.     

Steady‐State Modeling and Simulation of an Axial‐Radial Ammonia Synthesis Reactor

A two‐dimensional model was developed for an axial‐radial ammonia synthesis reactor of the Shiraz petrochemical plant. In this model, momentum and continuity equations as well as mass and energy balance equations are solved simultaneously by orthogonal collocation on the finite element method to obtain pressure, velocity, concentration and temperature profiles in both axial and radial directions. For the catalyst particle, the effectiveness factor is calculated by solving a two‐point boundary value differential equation. The boundary conditions for the Navier‐Stokes and continuity equations are obtained by using equations representing the phenomena of gases splitting or joining in different streams and going through holes in a thin wall. The results of the mathematical model have been compared with the plant data and a good agreement is obtained.     

A Thermo-Hydro-Mechanics Bidirectional Coupling Mathematical Model for Drying of Biological Porous Medium

Based on Fickian diffusion theory, Fourier's law of heat conduction and thermoelasticity mechanics, a thermo-hydro-mechanics bidirectional coupling mathematical model has been developed to simulate the hot air convective drying of biological porous media. The transient model, composed of a system of partial differential equations, was solved by finite difference methods. The numerical results were compared with available experimental data obtained during the drying of potatoes. The numerical results obtained using the mathematical model were in good agreement with the experimental data. Numerical simulations of the drying curve variations and the spatio-temporal distributions of moisture, temperature, and drying stresses and strains were evaluated.     

Simulation of rapid pressure swing adsorption and reaction processes

A general model for non-isothermal adsorption and reaction in a rapid pressure swing process is described. Several numerical discretisation methods for the solution of the model are compared. These include the methods of orthogonal collocation, orthogonal collocation on finite elements, double orthogonal collocation on finite elements, and cells-in-series. Computationally, orthogonal collocation on finite elements is found to be the most efficient of these. The model is applied to air separation for oxygen production. Calculations confirm the formation of a concentration shock when an adsorbent bed is pressurised with air. The form and propagation of the shock over short times is found to be in excellent agreement with the exact similarity transformation solutions derived for an infinitely long bed. For air separation, novel experimental measurements, showing an optimum particle size for maximum product oxygen purity, are accurately described by the model. Calculations indicate that a poor separation results from ineffective pressure swing for beds containing very small particles, and from intraparticle diffusional limitations for beds containing very large particles. For adsorption coupled with reaction, finite rate and reversible reactions are considered. These include both competitive and non-competitive reaction schemes. For the test case of a dilute reaction A &.rlhar2; B + 3C, with B the only adsorbing species, bed pressurisation calculations are found to be in excellent agreement with the solutions obtained by the method of characteristics.     

Multi-scale simulation of oblique collisions of a droplet on a surface in the Leidenfrost regime

This work illustrates the phenomena of oblique impact of a water droplet on a hot solid surface in the Leidenfrost regime using a multi-scale model. The flow and heat transfer behavior on the droplet scale as described by the macroscopic model is solved using the finite volume method, together with the level set and the immersed boundary methods which quantify the variations of the gas-liquid and fluid-solid interfaces. A micro-scale vapor layer model is used to account for the resistance effect of the vapor layer generated by the film-boiling evaporation. These two models are coupled in each time step, and solved concurrently. Based on this multi-scale model, the effect of the impact velocity is investigated numerically. The droplet shape and impact parameters such as momentum loss and contact time calculated from the present model are compared with the experimental results obtained from the literature. A good agreement is seen between the simulated and the experimental results.     

Experimental study and finite element simulation of a glass fiber fabric shaping process

A finite element simulation is proposed for the shaping of glass fiber fabric. The overall mechanical behavior of the fabric is obtained by combining the tensile behavior of a single thread and the current position of threads in the fabric. The constitutive model for a single thread in tension is based on a statistical approach and is identified using tensile tests. Shear and tensile tests have been carried out on fabric specimens to demonstrate that the behavior of the fabric mainly results from the contribution of each thread, the sliding between fiber threads having a small effect on the energy for the deformation mechanism of these fabrics. A numerical model for the shaping process is obtained based on a finite element approach using three- and four-node membrane shell elements. The formulation accounts for the large displacements and large strains involved in the process as well as the mechanical behavior. A drawing simulation is presented in the case of an hemispherical punch. The comparison with experimental results obtained in this case shows good agreement.     

Stress analysis of crazes at moving crack tips

Summary The finite element method is applied to contours of craze zones in front of moving crack tips in polymethylmethacrylate (PMMA), measured by interferometry, in order to compute the stress distribution. In contrast to the constant stress assumed in the Dugdale model, a stress distribution is found with a maximum at the crack tip then a sharp decrease and a more gradual decline over the larger part of the craze length. Computed stresses as well as the Dugdale stress increase with increasing crack speed and, hence, decreasing loading time. Generally the results obtained are in good agreement with those already found for growing crazes at stationary crack tips.     

Determination of lamella thickness distributions in isotactic polypropylene by X-ray line profile analysis

X-ray line profile analysis was used to determine the size distribution of the crystalline lamellae in isotactic polypropylene (iPP) assuming a log-normal size distribution. A comparison with the size distribution as determined by differential scanning calorimetry (DSC) yields an excellent agreement of both methods. It is noted that the agreement depends strongly on whether linear lattice defects, particularly dislocations are taken into account in the X-ray analysis. This is especially true for deformed iPP with a high number of deformation induced dislocations. It was also found that for a multimodal distribution of lamella thickness in the DSC experiment as induced by the introduction of titanium dioxide nanoparticles as filler material the lamella thickness distribution from X-ray profile analysis is still in good agreement with DSC although the model used was only monomodal.