<p>Coextrusion is the simultaneous extrusion from a single die of two or more homogeneous melts which form a lamellar structure. Each resin needs its own extruder and a single extruder can supply more than one layer of the same resin. In recent years, coextrusion has gained importance because it is an economical and effective method to obtain plastic products that meet specific market requirements. From the fluid mechanics point of view, one of the main features of the coextrusion process is the presence of internal interfaces (that separate the fluid phases) and contact lines (which are formed when an interface intersects the die wall). Two types of problems exist in the coextrusion process; interfacial flow instability and non-uniform layer thickness distribution. Non-uniform layer distribution refers to the change in thickness of the distribution of the layers across the width of the sheet. Interfacial flow instability appears as an unsteady waviness of the interface between the two polymers. Materials with different theological properties such as apparent viscosity, elasticity and shear stress effects, give rise to irregular interfaces, which lead to high scrap rates and undesired mechanical and optical properties. This work focuses on the problem of interfacial instability. The study examines the main parameters involved in coextrusion operations, i.e., die design, processing conditions and rheological properties of polymer systems, in order to understand both their influence on the interfacial instability and suggest ways to control the instability. By means of a transient solution, the interfacial stability of a given coextrusion flow system can be analyzed in terms of the evolution of the interface in time in response to a external perturbation. Two-dimensional time-dependent finite element solutions of the bi-component flow of Newtonian, generalized Newtonian (Carreau model) and viscoelastic (Criminale-Ericksen-Filbey or CEF) fluids in complex geometries (parallel plates, abrupt and tapered expansions and contractions, and a coat-hanger die geometry), are presented. For the case of Newtonian and generalized Newtonian fluid systems through parallel plates, solutions have been successfully compared against experimental data from the literature and previous results provided by linear stability analysis (LSA). An industrial problem has been studied and the numerical simulation of a two layer homopolymer LDPE 1321(TM) (Dow Chemical Co.) through a tear drop coat-hanger die has been carried out. Finally, CEF flow solutions show that for given elasticity, viscosity and flowrate ratios, the interface between the two fluids has an irregular shape even in the steady state. This anomaly at the interface is qualitatively similar to that observed in experimental results from unstable coextrusion samples.</p> / Doctor of Philosophy (PhD)

<p>The production of controlled-rheology polypropylene polymers by means of peroxide initiated degradation during reactive extrusion has been studied experimentally and numerically. Experiments were carried out using various amounts of a peroxide to promote chain scission reactions for the purpose of modifying the molecular weight distribution of commercial isotactic polypropylene resins. Experimental runs were carried out in a single screw plasticating extruder and in glass ampoules. The polymers produced were evaluated in terms of their molecular, rheological and mechanical properties. During the extruder runs the residence time distribution in the extruder screw channel was measured by using a radioactive tracer technique in order to study the effects of peroxide concentration, barrel temperature and screw speed.</p> <p>A fully-predictive mathematical model was developed for the peroxide degradation of polypropylene in a single-screw plasticating extruder. The model was developed using conventional plasticating extrusion theory and a simple set of chemical reactions which caused chain scission. The interactions of the flow and reaction phenomena were taken into account via residence time distribution and the chemorheology of the reactive melt. The model includes several submodels for the flow of solids in a feed hopper, flow in the solids conveying zone of the extruder, melting of the polymer, flow and reaction in the melt pumping zone and in the die region. Given the operating conditions and the geometrical configuration of the screw, the model can predict: the mass flow rate of the polymer, the pressure, temperature and molecular weight profiles along the screw channel and in the die, extrudate swell at the die exit and the residence time distribution of the material in the extruder channel. Model predictions are in good agreement with measurements on a 38 mm diameter extruder.</p> / Doctor of Philosophy (PhD)

<p>Flow phenomena associated with the injection mold filling process have a significant impact on the microstructure development and hence on the final properties of molded articles. The present work is concerned with the mathematical modeling and numerical simulation of the mold filling process. The aim is to provide in-depth understanding of the flow phenomena involved and investigate their impact on the microstructure of the molded polymer article.</p> <p>The mold filling process takes place as a rolling-type advancement of the flow front over the mold walls. The flow field behind the advancing flow front is known as fountain flow, and it is the salient feature of mold filling. The fountain flow phenomenon is examined extensively with finite element techniques, both in the steady-state and in the time domain. The u-v-p-h-δ formulation described in the present work is a powerful numerical technique for the simulation of free surface flows, and determines simultaneously the flow field and the free surface shape. Steady-state and transient simulations with Newtonian and shear-shinning fluids in planar and axisymmetric geometries are presented. Various features of fountain flow are described with the aid of velocity vector, pressure, free surface shape, and streamline plots. The general problem of fountain and reverse fountain flow (immiscible liquid displacement) and the collision of two flow fronts to form a weldline are also investigated.</p> <p>The deformation history experienced by the fluid due to fountain flow is examined on the basis of the numerically computed flow field, by tracking material elements as they move through the flow domain. It is found that material elements from the centerline migrate towards the mold walls, extend in the flow direction and form characteristic V-shapes, fully in agreement with available visualization experiments.</p> <p>A viscoelastic constitutive equation (multi-mode Leonov model) is introduced in order to investigate the effect of fountain flow on the molecular orientation of injection molded parts, as reflected in available birefringence measurements. A finite element algorithm for the numerical simulation of viscoelastic free surface flows is described. Fountain flow simulations are performed for material properties and processing conditions corresponding to available experiments. Finite element solutions are obtained at high levels of fluid elasticity and they converge with mesh refinement, provided that a slip boundary condition is applied at the wall to alleviate the stress singularities. The finite element results are combined with a simple theory to predict frozen-in stress and birefringence distributions. Computational results are compared to, and agree favorably with, available experimental data. It is demonstrated quantitatively that fountain flow is responsible for the molecular orientation pattern of the surface layer of injection molded parts. A viscoel~stic constitl1tive eq~ation (multi-mode Leonov model) is introduced in , order to investig'ate the effect of fountain flow on the molecular orientation of injectio~ molded parts, a~ refl~cted in available birefringence measurements. A finite element algorithm for the numerical simulation of viscoelastic fre~ surface flows 'is described. Fountain flow simulations are performed for material properties and processing conditions corresponding to available' experiments. Finite element ~olutionsare obtained at high levels of fluid elasticity and they converge with mesh refinement, provided that a slip boundary ..... condition is applied at the wall to alleviate the stress singularities. The finite element results are combined with a simple theory to predict frozen-in stress and birefringence d!stributions. Computational results are compared to, and agree favorably with, available experimental data. It is demonstrated quantitatively that fountain flow is responsible for the molecular orientation pattern of the surface layer ofinjection molded parts.</p> / Doctor of Philosophy (PhD)

<p>A pilot scale distillation column was built jointly with other students to study the separation of an azeotropic mixture of acetone and methanol. An extractive distillation process is used to break the azeotrope using water as a solvent. This is a nonideal, nonlinear, multicomponent system. A VAX 11/750 computer with DPM-23 industrial front-end system was used in a distributed control configuration for control and data archiving of the column. An on-line Varian-6000 gas chromatograph (G.C.) is used for the top and bottoms product analysis.</p> <p>A complete tray to tray steady state and dynamic mass and energy balance models were developed. The validity of these models has been explored using experimental data over a wide operating region. The simulated behaviour from the dynamic model was compared with the experimental column behaviour for various open loop steps in the reflux flow rate, feed flow rate, feed composition and reboiler duty. The nonlinear behaviour of the system was simulated by the models. A simple model for vapour liquid equilibrium (VLE) calculations was developed and its validity was proven.</p> <p>The grouping of several trays together as a compartment has a thermodynamic basis and reduces the total number of model equations to be solved. Models with 3, 4 and 5 compartments showed good agreement with the experimental data and with a tray to tray model. A saving of 70% in the computation time was achieved over the tray to tray model. The 5 compartment model was used to develop a reduced order bilinear model of the system using the reflux flow rate and the reboiler duty as manipulated variables. The dynamics of the column were investigated for steps in steam pressure, reflux flow rate and feed flow rate. The system behaviour using the bilinear model and a complete tray to tray model were similar to the actual plant data.</p> <p>PI control strategies were simulated for single and dual composition control for four different kinds of disturbances. From the simulation studies it was found that for the control strategy with two single loop the conventional pairing of the reflux flow rate and reboiler duty is suitable for only certain kinds of disturbances. Selection of the water flow rate and reboiler duty (steam pressure) as a manipulated variable pairing showed better performance. This was also shown experimentally.</p> <p>A bilinear optimal controller design was developed which would result in an asymptotically stable system. The optimal controller for a bilinear system is nonlinear in nature, but the control law depends upon the objective function selected. The proof of optimality is given. It was also shown that an optimal controller based on a bilinear equation has a larger region of application than a controller designed from a linearized model. The optimal controller, along with a reduced order bilinear model, was applied to a simulation and on the pilot plant for dual composition control. Reflux flow rate and reboiler duty were used as the manipulated variable pair. The weighting matrices from the objective function and the constant system matrices from the model were used to solve a Liapunov equation to obtained the matrix used in the control law. The tray temperatures were used to predict compositions for the experimental control studies. A recursive least squares (RLS) method was used to update the predictor parameters when the G.C. analyses were available. An optimal controller with the composition predictor was implemented successfully on the pilot scale extractive distillation column for the servo control problem. A bilinear controller was also applied to the regulatory problem of a feed flow disturbance. It is found that even a multivariable controller based on the reflux flow rate and reboiler duty did not perform well. Subsequently, a bilinear model for the extractive distillation was changed to use water flow rate and reboiler duty as manipulated variables. The controller resulting from this model was implemented successfully on the simulation for 20% feed flow disturbance. It should be noted that the system performance depends upon the performance index used in the design of the bilinear controller.</p> / Doctor of Philosophy (PhD)

<p>The objectives of the present study were to investigate, under laboratory conditions, the strength of coke as a function of some of the key variables in the carbonization process, including the addition of some inert carbonaceous materials, and to analyze the effects of these additions on the optical properties of a particular high fluidity coal (Devco). Three coals were selected; Devco, a Canadian coal, and Madison and Chisholm both of which are American coals. Three inert carbonaceous additives were used; Devco semicoke (carbonized at 500°C), low temperature Devco coke (carbonized at 700°C), and coke breeze.</p> <p>The experimental work was divided into two parts. In the first part, a full factorial design was planned and the blends of Devco coal were carbonized according to it. The variables investigated were: heating rate, size, amount, and 'type' of the inert carbonaceous blended. The dependent variable was the microstrength index (MSI). It was found that the 'type of inert' had the largest statistical weight on the results. The content and mean particle size of the additive in the blend and their interactions with the 'type' were also very significant in the strength. An empirical equation was obtained to express MSI as a function of these variables. In the second part, the blends of the three coals were carbonized according to another statistical design to investigate the following variables: heating rate, type of coal and type of inert. The 'type of coal' was found to be the most statistically significant variable. Nevertheless, the type of inert changed drastically the mechanical properties.</p> <p>In single coal experiments the blending of Devco semicoke-500°C increased the MSI (i.e., 10% addition raised the index in Madison by 28%, Chisholm by 28% and Devco by 18%). On the other hand, the blending of coke breeze caused the MSI to drop (10% addition reduced the index in Madison by 29%, Chisholm by 22% and Devco by 19%). The type of inert was characterized by its microhardness, true specific gravity, and ash and volatile matter contents. The type of coal was described by an empirical function derived from accepted industrial correlations.</p> <p>A relationship has been established between microstrength index and tensile strength based on data of the present work. Several samples of cokes were analyzed under the SEM and the optical microscope. It was observed that the addition of Devco semicoke-500° and low temperature Devco coke-700°C reduced the amount of isotropic carbon present in the structure; these blends also had the higher strength.</p> / Master of Engineering (ME)

<p>Three different control strategies are compared in the control of the output temperature and the total flowrate of a heat exchanger stirred tank process: single loop control, Davison's robust control and decoupling control.</p> <p>When the single loop control was applied, interactions between the process variables were observed when the flow setpoint was changed. This resulted in large oscillations in the temperature. The load responses were, however, satisfactory. It was shown that Davison's robust controller was similar to a static decoupler using two integral feedback controllers of the same gain. The integral mode alone was not found to be adequate for the control of the slow temperature process. Static decoupling gave satisfactory results for both setpoint and load changes. There was some improvement, although-not very great, when dynamic decoupling was applied. This was because the cross and direct dynamics of the temperature processes had approximate time constants.</p> / Master of Engineering (ME)

<p>An effective mathematical model for estimation for the Particle Size Distribution (PSD) in suspension copolymerization of styrene/divinylbenzene has been developed. Its effectiveness is shown as a compromise between a sound theoretical basis and the simplest possible mathematical structure, which makes possible the solution of the governing equations using conventional computational tools. In building the model, a comprehensive and systematic approach was undertaken. The first stage of this approach was to critically review and analyze the literature in suspension polymerization. The most important weaknesses and deficiencies of the existing models and the approaches used to build them were identified, and a strategy to overcome them was designed and implemented. The second stage of the approach was to identify the key factors that control the PSD, and build mechanistic mathematical models of an intermediate and balanced degree of complexity. The third stage consisted of incorporating these mechanistic models into a macro-scale model of the PSD. Using novel experimental design techniques, the relative importance of the different factors on the PSD, and the aspects of the model that needed refinement were determined. The final stage consisted of implementing changes to the model in a balanced and effective way. The result was an improved model for PSD that assigns adequate weight to the importance of each key factor, with similar degree of complexity as the best models reported in the literature, but better performance and increased reliability of predictions. Some of the contributions of this thesis to the field of Polymer Science and Engineering include: the development and validation of an effective model for crosslinking free-radical copolymerization kinetics; the establishment of prescriptions to guide the efforts in the acquisition and interpretation of information aimed at improving our understanding and modelling capabilities of suspension polymerization reactors; the inclusion, for the first time in suspension polymerization modelling, of non-homogenous mixing in the stirred tank reactor into the PSD model; the development of mathematical models for breakage and coalescence in liquid-liquid dispersions, and the systematic and effective use of mechanistic modelling for experimental design purposes in polymer production studies.</p> / Doctor of Philosophy (PhD)

<p>A numerical method has been developed to model the jet-to-jet impingement in a mixing head. The governing equations are discretized in non-orthogonal curvilinear coordinates and higher-order upwinding methods are used for convection term discretization. Several problems with known solutions are used to test accuracy of the method. The results show that the method can predict the flow fields at moderate and high Reynolds numbers accurately.</p> <p>The opposed jet flow field is used by the reaction injection moulding mixhead to mix pre-polymers. The stready state flow field exists at Reynolds numbers below 90 and unsteady state exists at Reynolds numbers above 90. The results of numerical simulations show that at the Reynolds number 50, the flow field is symmetrical and rotating ring vortices are formed around the impingement point. Symmetry breaks down as the Reynolds number is raised. Time integration showed that the flow field oscillates at Reynolds numbers above 100 and multiple frequencies exist at the Reynolds number of 125. The results are consistent with experimental results.</p> <p>In the last chapter, the dynamical system theory is used to examine the opposed jet flow field. The stagnation point is a hyperbolic point of a dynamical system and can promote mixing. The elliptic points which exist at the core of vortices hinder mixing. The (D:D)1/2 field was evaluated and confirmed the results of the dynamical system theory. The area surrounding the hyperbolic point had highest (D:D)1/2 values indicating that the flow field can stretch more efficiently. A flow pattern which consists of multiple hyperbolic points is proposed as an alternate design for the mixhead.</p> / Doctor of Philosophy (PhD)

<p>The laminar flow field in a Kenics KM® static mixer and a Werner and Pfleiderer ZSK-30® twin screw extruder (TSE) has been studied using laser induced fluorescence (LIF) coupled with digital image analysis, particle image velocimetry (PIV) and laser Doppler anemometry (LDA). The objective of this study was to observe the flow fields in these two devices, to determine their mixing capabilities qualitatively and quantitatively. Mixing in the static mixer was quantified by measurement of the number average striation thickness, variance of striation widths and interfacial area for elements with 90 degrees of twist. From flow visualisation and LDA measurements, transitions were observed in the flow where vortices developed above the first and second elements. These vortices did not appreciably enhance mixing after 4 to 5 elements with an aspect ratio (L/D) of 1.0. The velocity field measured over the first four elements (L/D = 1.5), captured the mixing nature of the static mixer, where flow was split at the leading edge and recombined at the trailing edge of the elements. Recirculations in the radial plane were observed where fluid flowed from the high-pressure side of the element forward out along the tube wall to the low-pressure side or suction side. The radial flow field required a development length to allow the flow to build in magnitude. The rate of deformation analysis on the flow field indicated that mixing efficiency would be increased if the first element had a larger helix angle. The highest rates of deformation were measured at the junctions between elements, and between the element and tube surfaces. The visualisations coupled with image analysis for the TSE demonstrated clearly that the mixing was enhanced by placing a reverse conveying element directly after the last set of kneading discs in the mixing section. The velocity results for the screw profile with extended first and last discs (geometry A) showed an increase in back flow and recirculations with increasing screw rotation. When a forward conveying element was used before and after the kneading discs (geometry B), higher radial and lower axial velocities were measured. The fluid in the direction of rotation and no back-mixing or recirculations in the flow were measured. Results of a 3D model for the simulation of flow in the kneading disc region and the PIV measurements were compared. Results for geometry A are in good qualitative agreement for low flow rates. Geometry B showed better agreement at higher flow rates compared to lower flow rates. The performance of the kneading discs were characterized based on the shear, elongation and the magnitude of the rate of deformation tensor within the measured flow fields. For the various cases of screw rotation speed, the largest rates of deformations (elongation and shear) were seen at the first and last disc of the kneading block where transitions occurred.</p> / Doctor of Philosophy (PhD)

<p>This thesis considers the utilization of historical process data for three different process engineering problems. Latent variable methods such as Principal Components Analysis (PCA) and Partial Least Squares (PLS) are shown to be key tools for dealing with the highly correlated variables typically found in process operating data and for ensuring feasibility of the solutions. The restrictions and limitations encountered by any databased approach are recognized and discussed. The problem of designing process conditions that yield a new product grade quality within the range of already existing grades is addressed by latent variable regression models and their inversion. Latent variable techniques allow for models that not only describe the relationship between process conditions. This leads to the design of new conditions that are consistent with the plant operations from the past. Feasibility issues of both the new quality specifications as well as the predicted operating conditions are addressed. The approach is illustrated on a simulated process and three industrial processes. The related topic of moving the production of a particular product grade from a plant A to another plant B when both plants have already produced a similar range of grades is treated as well. Since the two plants may differ in size, configuration etc. the process conditions for one grade may be very different in the two plants. A latent variable method is proposed which uses data from both plants to predict process conditions for plant B for a grade previously produced only in plant A. The issue of feasibility is again addressed for both product quality and process conditions. The last part of the thesis explores the problematic issue of utilizing large process operating databases for process performance improvement. The major problem found with using normal operating data for this purpose is correlation among manipulated variables and disturbances as caused by feedback operation or other operating strategies. Such correlation is shown to impede the extraction of causal information from the database, which is necessary in order to infer better process conditions. This implies that only in exceptional circumstances would it be feasible to use empirical databased methods for process optimization.</p> / Doctor of Philosophy (PhD)