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.

Heat transfer in microwave heating

Heat transfer is considered as one of the most critical issues for design and implement of large-scale microwave heating systems, in which improvement of the microwave absorption of materials and suppression of uneven temperature distribution are the two main objectives. The present work focuses on the analysis of heat transfer in microwave heating for achieving highly efficient microwave assisted steelmaking through the investigations on the following aspects: (1) characterization of microwave dissipation using the derived equations, (2) quantification of magnetic loss, (3) determination of microwave absorption properties of materials, (4) modeling of microwave propagation, (5) simulation of heat transfer, and (6) improvement of microwave absorption and heating uniformity. Microwave heating is attributed to the heat generation in materials, which depends on the microwave dissipation. To theoretically characterize microwave heating, simplified equations for determining the transverse electromagnetic mode (TEM) power penetration depth, microwave field attenuation length, and half-power depth of microwaves in materials having both magnetic and dielectric responses were derived. It was followed by developing a simplified equation for quantifying magnetic loss in materials under microwave irradiation to demonstrate the importance of magnetic loss in microwave heating. The permittivity and permeability measurements of various materials, namely, hematite, magnetite concentrate, wüstite, and coal were performed. Microwave loss calculations for these materials were carried out. It is suggested that magnetic loss can play a major role in the heating of magnetic dielectrics. Microwave propagation in various media was predicted using the finite-difference time-domain method. For lossy magnetic dielectrics, the dissipation of microwaves in the medium is ascribed to the decay of both electric and magnetic fields. The heat transfer process in microwave heating of magnetite, which is a typical magnetic dielectric, was simulated by using an explicit finite-difference approach. It is demonstrated that the heat generation due to microwave irradiation dominates the initial temperature rise in the heating and the heat radiation heavily affects the temperature distribution, giving rise to a hot spot in the predicted temperature profile. Microwave heating at 915 MHz exhibits better heating homogeneity than that at 2450 MHz due to larger microwave penetration depth. To minimize/avoid temperature nonuniformity during microwave heating the optimization of object dimension should be considered. The calculated reflection loss over the temperature range of heating is found to be useful for obtaining a rapid optimization of absorber dimension, which increases microwave absorption and achieves relatively uniform heating. To further improve the heating effectiveness, a function for evaluating absorber impedance matching in microwave heating was proposed. It is found that the maximum absorption is associated with perfect impedance matching, which can be achieved by either selecting a reasonable sample dimension or modifying the microwave parameters of the sample.

Maximum principle preserving high order schemes for convection-dominated diffusion equations

The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO scheme, and then propose a new parametrized MPP high order finite difference(FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains the third order accuracy without extra CFL constraint when the low order monotone flux is chosen appropriately. Numerical tests in both one and two dimensional cases are performed on the simulation of the incompressible Navier-Stokes equations in vorticity stream-function formulation and several other problems to show the effectiveness of the proposed method.

Study of and design procedure for dual circularly polarized waveguide slot arrays

For the past sixty years, waveguide slot radiator arrays have played a critical role in microwave radar and communication systems. They feature a well-characterized antenna element capable of direct integration into a low-loss feed structure with highly developed and inexpensive manufacturing processes. Waveguide slot radiators comprise some of the highest performance—in terms of side-lobe-level, efficiency, etc. — antenna arrays ever constructed. A wealth of information is available in the open literature regarding design procedures for linearly polarized waveguide slots. By contrast, despite their presence in some of the earliest published reports, little has been presented to date on array designs for circularly polarized (CP) waveguide slots. Moreover, that which has been presented features a classic traveling wave, efficiency-reducing beam tilt. This work proposes a unique CP waveguide slot architecture which mitigates these problems and a thorough design procedure employing widely available, modern computational tools. The proposed array topology features simultaneous dual-CP operation with grating-lobe-free, broadside radiation, high aperture efficiency, and good return loss. A traditional X-Slot CP element is employed with the inclusion of a slow wave structure passive phase shifter to ensure broadside radiation without the need for performance-limiting dielectric loading. It is anticipated this technology will be advantageous for upcoming polarimetric radar and Ka-band SatCom systems. The presented design methodology represents a philosophical shift away from traditional waveguide slot radiator design practices. Rather than providing design curves and/or analytical expressions for equivalent circuit models, simple first-order design rules – generated via parametric studies — are presented with the understanding that device optimization and design will be carried out computationally. A unit-cell, S-parameter based approach provides a sufficient reduction of complexity to permit efficient, accurate device design with attention to realistic, application-specific mechanical tolerances. A transparent, start-to-finish example of the design procedure for a linear sub-array at X-Band is presented. Both unit cell and array performance is calculated via finite element method simulations. Results are confirmed via good agreement with finite difference, time domain calculations. Array performance exhibiting grating-lobe-free, broadside-scanned, dual-CP radiation with better than 20 dB return loss and over 75% aperture efficiency is presented.

Influence of Mechanical and Thermal Boundary Conditions on Stabilizing/Destabilizing Mechanisms in Evaporating Liquid Films

Liquid films, evaporating or non-evaporating, are ubiquitous in nature and technology. The dynamics of evaporating liquid films is a study applicable in several industries such as water recovery, heat exchangers, crystal growth, drug design etc. The theory describing the dynamics of liquid films crosses several fields such as engineering, mathematics, material science, biophysics and volcanology to name a few. Interfacial instabilities typically manifest by the undulation of an interface from a presumed flat state or by the onset of a secondary flow state from a primary quiescent state or both. To study the instabilities affecting liquid films, an evaporating/non-evaporating Newtonian liquid film is subject to a perturbation. Numerical analysis is conducted on configurations of such liquid films being heated on solid surfaces in order to examine the various stabilizing and destabilizing mechanisms that can cause the formation of different convective structures. These convective structures have implications towards heat transfer that occurs via this process. Certain aspects of this research topic have not received attention, as will be obvious from the literature review. Static, horizontal liquid films on solid surfaces are examined for their resistance to long wave type instabilities via linear stability analysis, method of normal modes and finite difference methods. The spatiotemporal evolution equation, available in literature, describing the time evolution of a liquid film heated on a solid surface, is utilized to analyze various stabilizing/destabilizing mechanisms affecting evaporating and non-evaporating liquid films. The impact of these mechanisms on the film stability and structure for both buoyant and non-buoyant films will be examined by the variation of mechanical and thermal boundary conditions. Films evaporating in zero gravity are studied using the evolution equation. It is found that films that are stable to long wave type instabilities in terrestrial gravity are prone to destabilization via long wave instabilities in zero gravity.

Study of particle movement in the nearshore region of Lake Superior with radioisotope tracers

Biogeochemical processes in the coastal region, including the coastal area of the Great Lakes, are of great importance due to the complex physical, chemical and biological characteristics that differ from those on either the adjoining land or open water systems. Particle-reactive radioisotopes, both naturally occurring (210Pb, 210Po and 7Be) and man-made (137Cs), have proven to be useful tracers for these processes in many systems. However, a systematic isotope study on the northwest coast of the Keweenaw Peninsula in Lake Superior has not yet been performed. In this dissertation research, field sampling, laboratory measurements and numerical modeling were conducted to understand the biogeochemistry of the radioisotope tracers and some particulate-related coastal processes. In the first part of the dissertation, radioisotope activities of 210Po and 210Pb in a variability of samples (dissolved, suspended particle, sediment trap materials, surficial sediment) were measured. A completed picture of the distribution and disequilibrium of this pair of isotopes was drawn. The application of a simple box model utilizing these field observations reveals short isotope residence times in the water column and a significant contribution of sediment resuspension (for both particles and isotopes). The results imply a highly dynamic coastal region. In the second part of this dissertation, this conclusion is examined further. Based on intensive sediment coring, the spatial distribution of isotope inventories (mainly 210Pb, 137Cs and 7Be) in the nearshore region was determined. Isotope-based focusing factors categorized most of the sampling sites as non- or temporary depositional zones. A twodimensional steady-state box-in-series model was developed and applied to individual transects with the 210Pb inventories as model input. The modeling framework included both water column and upper sediments down to the depth of unsupported 210Pb penetration. The model was used to predict isotope residence times and cross-margin fluxes of sediments and isotopes at different locations along each transect. The time scale for sediment focusing from the nearshore to offshore regions of the transect was on the order of 10 years. The possibility of sediment longshore movement was indicated by high inventory ratios of 137Cs: 210Pb. Local deposition of fine particles, including fresh organic carbon, may explain the observed distribution of benthic organisms such as Diporeia. In the last part of this dissertation, isotope tracers, 210Pb and 210Po, were coupled into a hydrodynamic model for Lake Superior. The model was modified from an existing 2-D finite difference physical-biological model which has previously been successfully applied on Lake Superior. Using the field results from part one of this dissertation as initial conditions, the model was used to predict the isotope distribution in the water column; reasonable results were achieved. The modeling experiments demonstrated the potential for using a hydrodynamic model to study radioisotope biogeochemistry in the lake, although further refinements are necessary.