Three dimensional finite element simulation of polymer melting and flow in a single-screw extruder : optimization of screw channel geometry

Single-screw extrusion is one of the widely used processing methods in plastics industry, which was the third largest manufacturing industry in the United States in 2007 [5]. In order to optimize the single-screw extrusion process, tremendous efforts have been devoted for development of accurate models in the last fifty years, especially for polymer melting in screw extruders. This has led to a good qualitative understanding of the melting process; however, quantitative predictions of melting from various models often have a large error in comparison to the experimental data. Thus, even nowadays, process parameters and the geometry of the extruder channel for the single-screw extrusion are determined by trial and error. Since new polymers are developed frequently, finding the optimum parameters to extrude these polymers by trial and error is costly and time consuming. In order to reduce the time and experimental work required for optimizing the process parameters and the geometry of the extruder channel for a given polymer, the main goal of this research was to perform a coordinated experimental and numerical investigation of melting in screw extrusion. In this work, a full three-dimensional finite element simulation of the two-phase flow in the melting and metering zones of a single-screw extruder was performed by solving the conservation equations for mass, momentum, and energy. The only attempt for such a three-dimensional simulation of melting in screw extruder was more than twenty years back. However, that work had only a limited success because of the capability of computers and mathematical algorithms available at that time. The dramatic improvement of computational power and mathematical knowledge now make it possible to run full 3-D simulations of two-phase flow in single-screw extruders on a desktop PC. In order to verify the numerical predictions from the full 3-D simulations of two-phase flow in single-screw extruders, a detailed experimental study was performed. This experimental study included Maddock screw-freezing experiments, Screw Simulator experiments and material characterization experiments. Maddock screw-freezing experiments were performed in order to visualize the melting profile along the single-screw extruder channel with different screw geometry configurations. These melting profiles were compared with the simulation results. Screw Simulator experiments were performed to collect the shear stress and melting flux data for various polymers. Cone and plate viscometer experiments were performed to obtain the shear viscosity data which is needed in the simulations. An optimization code was developed to optimize two screw geometry parameters, namely, screw lead (pitch) and depth in the metering section of a single-screw extruder, such that the output rate of the extruder was maximized without exceeding the maximum temperature value specified at the exit of the extruder. This optimization code used a mesh partitioning technique in order to obtain the flow domain. The simulations in this flow domain was performed using the code developed to simulate the two-phase flow in single-screw extruders.

Automated optimization of polymer extrusion dies using finite element analysis

An extrusion die is used to continuously produce parts with a constant cross section; such as sheets, pipes, tire components and more complex shapes such as window seals. The die is fed by a screw extruder when polymers are used. The extruder melts, mixes and pressures the material by the rotation of either a single or double screw. The polymer can then be continuously forced through the die producing a long part in the shape of the die outlet. The extruded section is then cut to the desired length. Generally, the primary target of a well designed die is to produce a uniform outlet velocity without excessively raising the pressure required to extrude the polymer through the die. Other properties such as temperature uniformity and residence time are also important but are not directly considered in this work. Designing dies for optimal outlet velocity variation using simple analytical equations are feasible for basic die geometries or simple channels. Due to the complexity of die geometry and of polymer material properties design of complex dies by analytical methods is difficult. For complex dies iterative methods must be used to optimize dies. An automated iterative method is desired for die optimization. To automate the design and optimization of an extrusion die two issues must be dealt with. The first is how to generate a new mesh for each iteration. In this work, this is approached by modifying a Parasolid file that describes a CAD part. This file is then used in a commercial meshing software. Skewing the initial mesh to produce a new geometry was also employed as a second option. The second issue is an optimization problem with the presence of noise stemming from variations in the mesh and cumulative truncation errors. In this work a simplex method and a modified trust region method were employed for automated optimization of die geometries. For the trust region a discreet derivative and a BFGS Hessian approximation were used. To deal with the noise in the function the trust region method was modified to automatically adjust the discreet derivative step size and the trust region based on changes in noise and function contour. Generally uniformity of velocity at exit of the extrusion die can be improved by increasing resistance across the die but this is limited by the pressure capabilities of the extruder. In optimization, a penalty factor that increases exponentially from the pressure limit is applied. This penalty can be applied in two different ways; the first only to the designs which exceed the pressure limit, the second to both designs above and below the pressure limit. Both of these methods were tested and compared in this work.

Muffler characterization with implementation of the finite element method and experimental techniques

Determining how an exhaust system will perform acoustically before a prototype muffler is built can save the designer both a substantial amount of time and resources. In order to effectively use the simulation tools available it is important to understand what is the most effective tool for the intended purpose of analysis as well as how typical elements in an exhaust system affect muffler performance. An in-depth look at the available tools and their most beneficial uses are presented in this thesis. A full parametric study was conducted using the FEM method for typical muffler elements which was also correlated to experimental results. This thesis lays out the overall ground work on how to accurately predict sound pressure levels in the free field for an exhaust system with the engine properties included. The accuracy of the model is heavily dependent on the correct temperature profile of the model in addition to the accuracy of the source properties. These factors will be discussed in detail and methods for determining them will be presented. The secondary effects of mean flow, which affects both the acoustical wave propagation and the flow noise generation, will be discussed. Effective ways for predicting these secondary effects will be described. Experimental models will be tested on a flow rig that showcases these phenomena.

Laminar flow of a gas in a tube with large temperature differences.

The laminar low Mach number flow of a gas in a tube is analyzed for very small and very large values of the inlet-to-wall temperature ratio. When this ratio tends to zero, pressure forces confine the cold gas to a thin core around the axis of the tube. This core is neatly bounded by an ablation front that consumes it at a finite distance from the tube inlet. When the temperature ratio tends to infinity, the temperature of the gas increases smoothly from the wall to the axis of the tube and the shear stress and heat flux are positive at the wall despite the fact that the viscosity and thermal conductivity of the gas scaled with their inlet values tend to zero at the wall

High temperature micropillar compression of Al/SiC nanolaminates

The effect of the temperature on the compressive stress–strain behavior of Al/SiC nanoscale multilayers was studied by means of micropillar compression tests at 23 °C and 100 °C. The multilayers (composed of alternating layers of 60 nm in thickness of nanocrystalline Al and amorphous SiC) showed a very large hardening rate at 23 °C, which led to a flow stress of 3.1 ± 0.2 GPa at 8% strain. However, the flow stress (and the hardening rate) was reduced by 50% at 100 °C. Plastic deformation of the Al layers was the dominant deformation mechanism at both temperatures, but the Al layers were extruded out of the micropillar at 100 °C, while Al plastic flow was constrained by the SiC elastic layers at 23 °C. Finite element simulations of the micropillar compression test indicated the role played by different factors (flow stress of Al, interface strength and friction coefficient) on the mechanical behavior and were able to rationalize the differences in the stress–strain curves between 23 °C and 100 °C.

Finite volume modelling of an icefield with subglacial lake

Momentum, mass and energy balance laws provide the tools for the study of the evolution of an icefield covering a subglacial lake. The ice is described as a non-Newtonian fluid with a power-law constitutive relationship with temperature- and stress-dependent viscosity (Glen?s law) [1]. The phase transition mechanisms at the air/ice and ice/water interfaces yield moving boundary formulations, and lake hydrodynamics requires equation reduction for treating the turbulence.

Heated fiber optic distributed temperature sensing for measuring soil volumetric heat capacity and water content: A dual probe heat-pulse approach

The first feasibility study of using dual-probe heated fiber optics with distributed temperature sensing to measure soil volumetric heat capacity and soil water content is presented. Although results using different combinations of cables demonstrate feasibility, further work is needed to gain accuracy, including a model to account for the finite dimension and the thermal influence of the probes. Implementation of the dual-probe heat-pulse (DPHP) approach for measurement of volumetric heat capacity (C) and water content (θ) with distributed temperature sensing heated fiber optic (FO) systems presents an unprecedented opportunity for environmental monitoring (e.g., simultaneous measurement at thousands of points). We applied uniform heat pulses along a FO cable and monitored the thermal response at adjacent cables. We tested the DPHP method in the laboratory using multiple FO cables at a range of spacings. The amplitude and phase shift in the heat signal with distance was found to be a function of the soil volumetric heat capacity. Estimations of C at a range of moisture contents (θ = 0.09– 0.34 m3 m−3) suggest the feasibility of measurement via responsiveness to the changes in θ, although we observed error with decreasing soil water contents (up to 26% at θ = 0.09 m3 m−3). Optimization will require further models to account for the finite radius and thermal influence of the FO cables. Although the results indicate that the method shows great promise, further study is needed to quantify the effects of soil type, cable spacing, and jacket configurations on accuracy.

Third-generation synchrotron x-ray diffraction of 6-μm crystal of raite, ≈Na3Mn3Ti0.25Si8O20(OH)2⋅10H2O, opens up new chemistry and physics of low-temperature minerals

The crystal structure of raite was solved and refined from data collected at Beamline Insertion Device 13 at the European Synchrotron Radiation Facility, using a 3 × 3 × 65 μm single crystal. The refined lattice constants of the monoclinic unit cell are a = 15.1(1) Å; b = 17.6(1) Å; c = 5.290(4) Å; β = 100.5(2)°; space group C2/m. The structure, including all reflections, refined to a final R = 0.07. Raite occurs in hyperalkaline rocks from the Kola peninsula, Russia. The structure consists of alternating layers of a hexagonal chicken-wire pattern of 6-membered SiO4 rings. Tetrahedral apices of a chain of Si six-rings, parallel to the c-axis, alternate in pointing up and down. Two six-ring Si layers are connected by edge-sharing octahedral bands of Na+ and Mn3+ also parallel to c. The band consists of the alternation of finite Mn–Mn and Na–Mn–Na chains. As a consequence of the misfit between octahedral and tetrahedral elements, regions of the Si–O layers are arched and form one-dimensional channels bounded by 12 Si tetrahedra and 2 Na octahedra. The channels along the short c-axis in raite are filled by isolated Na(OH,H2O)6 octahedra. The distorted octahedrally coordinated Ti4+ also resides in the channel and provides the weak linkage of these isolated Na octahedra and the mixed octahedral tetrahedral framework. Raite is structurally related to intersilite, palygorskite, sepiolite, and amphibole.

Finite-size scaling analysis of the distributions of pseudo-critical temperatures in spin glasses

Using the results of large scale numerical simulations we study the probability distribution of the pseudo critical temperature for the three dimensional Edwards Anderson Ising spin glass and for the fully connected Sherrington-Kirkpatrick model. We find that the behaviour of our data is nicely described by straightforward finitesize scaling relations.

Phase transition in the three dimensional Heisenberg spin glass: Finite-size scaling analysis

We have investigated the phase transition in the Heisenberg spin glass using massive numerical simulations to study very large sizes, 483. A finite-size scaling analysis indicates that the data are compatible with the most economical scenario: a common transition temperature for spins and chiralities.

Finite Element Analysis of Thermal Buckling in Auotmotive Clutch and Brake Discs

Thermal buckling behavior of automotive clutch and brake discs is studied by making the use of finite element method. It is found that the temperature distribution along the radius and the thickness affects the critical buckling load considerably. The results indicate that a monotonic temperature profile leads to a coning mode with the highest temperature located at the inner radius. Whereas a temperature profile with the maximum temperature located in the middle leads to a dominant non-axisymmetric buckling mode, which results in a much higher buckling temperature. A periodic variation of temperature cannot lead to buckling. The temperature along the thickness can be simplified by the mean temperature method in the single material model. The thermal buckling analysis of friction discs with friction material layer, cone angle geometry and fixed teeth boundary conditions are also studied in detail. The angular geometry and the fixed teeth can improve the buckling temperature significantly. Young’s Modulus has no effect when single material is applied in the free or restricted conditions. Several equations are derived to validate the result. Young’s modulus ratio is a useful factor when the clutch has several material layers. The research findings from this paper are useful for automotive clutch and brake discs design against structural instability induced by thermal buckling.

Theoretical and numerical analysis of large-scale heat transfer problems with temperature-dependent pore-fluid densities

Purpose - In many scientific and engineering fields, large-scale heat transfer problems with temperature-dependent pore-fluid densities are commonly encountered. For example, heat transfer from the mantle into the upper crust of the Earth is a typical problem of them. The main purpose of this paper is to develop and present a new combined methodology to solve large-scale heat transfer problems with temperature-dependent pore-fluid densities in the lithosphere and crust scales. Design/methodology/approach - The theoretical approach is used to determine the thickness and the related thermal boundary conditions of the continental crust on the lithospheric scale, so that some important information can be provided accurately for establishing a numerical model of the crustal scale. The numerical approach is then used to simulate the detailed structures and complicated geometries of the continental crust on the crustal scale. The main advantage in using the proposed combination method of the theoretical and numerical approaches is that if the thermal distribution in the crust is of the primary interest, the use of a reasonable numerical model on the crustal scale can result in a significant reduction in computer efforts. Findings - From the ore body formation and mineralization points of view, the present analytical and numerical solutions have demonstrated that the conductive-and-advective lithosphere with variable pore-fluid density is the most favorite lithosphere because it may result in the thinnest lithosphere so that the temperature at the near surface of the crust can be hot enough to generate the shallow ore deposits there. The upward throughflow (i.e. mantle mass flux) can have a significant effect on the thermal structure within the lithosphere. In addition, the emplacement of hot materials from the mantle may further reduce the thickness of the lithosphere. Originality/value - The present analytical solutions can be used to: validate numerical methods for solving large-scale heat transfer problems; provide correct thermal boundary conditions for numerically solving ore body formation and mineralization problems on the crustal scale; and investigate the fundamental issues related to thermal distributions within the lithosphere. The proposed finite element analysis can be effectively used to consider the geometrical and material complexities of large-scale heat transfer problems with temperature-dependent fluid densities.

The adsorption of water in finite carbon pores

Grand canonical Monte Carlo simulations were applied to the adsorption of SPCE model water in finite graphitic pores with different configurations of carbonyl functional groups on only one surface and several pore sizes. It was found that almost all finite pores studied exhibit capillary condensation behaviour preceded by adsorption around the functional groups. Desorption showed the reverse transitions from a filled to a near empty pore resulting in a clear hysteresis loop in all pores except for some of the configurations of the 1.0nm pore. Carbonyl configurations had a strong effect on the filling pressure of all pores except, in some cases, in 1.0nm pores. A decrease in carbonyl neighbour density would result in a higher filling pressure. The emptying pressure was negligibly affected by the configuration of functional groups. Both the filling and emptying pressures increased with increasing pore size but the effect on the emptying pressure was much less. At pressures lower than the pore filling pressure, the adsorption of water was shown to have an extremely strong dependence on the neighbour density with adsorption changing from Type IV to Type III to linear as the neighbour density decreased. The isosteric heat was also calculated for these configurations to reveal its strong dependence on the neighbour density. These results were compared with literature experimental results for water and carbon black and found to qualitatively agree.

Finite-connectivity spin-glass phase diagrams and low-density parity check codes

We obtain phase diagrams of regular and irregular finite-connectivity spin glasses. Contact is first established between properties of the phase diagram and the performance of low-density parity check (LDPC) codes within the replica symmetric (RS) ansatz. We then study the location of the dynamical and critical transition points of these systems within the one step replica symmetry breaking theory (RSB), extending similar calculations that have been performed in the past for the Bethe spin-glass problem. We observe that the location of the dynamical transition line does change within the RSB theory, in comparison with the results obtained in the RS case. For LDPC decoding of messages transmitted over the binary erasure channel we find, at zero temperature and rate R=14, an RS critical transition point at pc 0.67 while the critical RSB transition point is located at pc 0.7450±0.0050, to be compared with the corresponding Shannon bound 1-R. For the binary symmetric channel we show that the low temperature reentrant behavior of the dynamical transition line, observed within the RS ansatz, changes its location when the RSB ansatz is employed; the dynamical transition point occurs at higher values of the channel noise. Possible practical implications to improve the performance of the state-of-the-art error correcting codes are discussed. © 2006 The American Physical Society.

Finitely coordinated models for low-temperature phases of amorphous systems

We introduce models of heterogeneous systems with finite connectivity defined on random graphs to capture finite-coordination effects on the low-temperature behaviour of finite-dimensional systems. Our models use a description in terms of small deviations of particle coordinates from a set of reference positions, particularly appropriate for the description of low-temperature phenomena. A Born-von Karman-type expansion with random coefficients is used to model effects of frozen heterogeneities. The key quantity appearing in the theoretical description is a full distribution of effective single-site potentials which needs to be determined self-consistently. If microscopic interactions are harmonic, the effective single-site potentials turn out to be harmonic as well, and the distribution of these single-site potentials is equivalent to a distribution of localization lengths used earlier in the description of chemical gels. For structural glasses characterized by frustration and anharmonicities in the microscopic interactions, the distribution of single-site potentials involves anharmonicities of all orders, and both single-well and double-well potentials are observed, the latter with a broad spectrum of barrier heights. The appearance of glassy phases at low temperatures is marked by the appearance of asymmetries in the distribution of single-site potentials, as previously observed for fully connected systems. Double-well potentials with a broad spectrum of barrier heights and asymmetries would give rise to the well-known universal glassy low-temperature anomalies when quantum effects are taken into account. © 2007 IOP Publishing Ltd.