Simulating polymer processes

The method of simulation selected is the Radial Functions Method that has shown to deliver excellent results for highly non-linear problems. This method has recently applied to model and simulate polymer processing problems by Lopez, Osswald, Estrada [2,3,4] and Mai-Duy [9] An additional motivation in this work is the... 

The thermal conductivity of polymeric fluids is very low and hence the main heat transport mechanism in polymer processing flows is convection (i.e. corresponds to very high Peclet numbers the Peclet number is defined as pcUUk which represents the ratio of convective to conductive energy transport). As emphasized before, numerical simulation of convection-dominated transport phenomena by the standard Galerkin method in a fixed (i.e. Eulerian) framework gives unstable and oscillatory results and cannot be used. 

Families of finite elements and their corresponding shape functions, schemes for derivation of the elemental stiffness equations (i.e. the working equations) and updating of non-linear physical parameters in polymer processing flow simulations have been discussed in previous chapters. However, except for a brief explanation in the worked examples in Chapter 2, any detailed discussion of the numerical solution of the global set of algebraic equations has, so far, been avoided. We now turn our attention to this important topic. 

Iterative solution methods are more effective for problems arising in solid mechanics and are not a common feature of the finite element modelling of polymer processes. However, under certain conditions they may provide better computer economy than direct methods. In particular, these methods have an inherent compatibility with algorithms used for parallel processing and hence are potentially more suitable for three-dimensional flow modelling. In this chapter we focus on the direct methods commonly used in flow simulation models. 

The utilization of commercially available finite element packages in the simulation of routine operations in industrial polymer processing is well established. However, these packages cannot be usually used as general research tools. Thus flexible in-house -created programs are needed to carry out the analysis required in the investigation, design and development of novel equipment and operations. 

The modern discipline of Materials Science and Engineering can be described as a search for experimental and theoretical relations between a material s processing, its resulting microstructure, and the properties arising from that microstructure. These relations are often complicated, and it is usually difficult to obtain closed-form solutions for them. For that reason, it is often attractive to supplement experimental work in this area with numerical simulations. During the past several years, we have developed a general finite element computer model which is able to capture the essential aspects of a variety of nonisothermal and reactive polymer processing operations. This "flow code" has been Implemented on a number of computer systems of various sizes, and a PC-compatible version is available on request. This paper is intended to outline the fundamentals which underlie this code, and to present some simple but illustrative examples of its use. 

We have begun to include detailed automatic alarm-handling in our control schemes, in order to begin unattended, eventually overnight operation. At present, any polymerization requiring more than one work day must be stopped and restarted on a second day. This prevents us from accurately simulating plant processes extending over more than one shift. Safe, unattended automatic lab reactor automation should, then, improve scale-up efficiency for many of our polymers. 

Real polymer processes involved in polymer crystallization are those at the crystal-melt or crystal-solution interfaces and inevitably 3D in nature. Before attacking our final target, the simulation of polymer crystallization from the melt, we studied crystallization of a single chain in a vacuum adsorption and folding at the growth front. The polymer molecule we considered was the same as described above a completely flexible chain composed of 500 or 1000 CH2 beads. We consider crystallization in a vacuum or in an extremely poor solvent condition. Here we took the detailed interaction between the chain molecule and the substrate atoms through Eqs. 8-10. 

Altinkaynak, A., Gupta, M., Spalding, M. A., and Crabtree, S. L., Melting in a Single-Screw Extruder Experiments and 3D Einite Element Simulations, Int. Polym. Process., 26, 182 (2011)... 

Two calculations are often used to evaluate the mixing in polymer processes. The first is the generation of surface area as simulated in two dimensions by the stretching of a line. The second is the standard deviation of the concentration of the minor component in a residence-time evaluation of the mixing process. This section will present both calculations. 

Today, the most widely used model simplification in polymer processing simulation is the Hele-Shaw model [5], It applies to flows in "narrow" gaps such as injection mold filling, compression molding, some extrusion dies, extruders, bearings, etc. The major assumptions for the lubrication approximation are that the gap is small, such that h < . L, and that the gaps vary slowly such that... 

Polymer processing modeling and simulation / Tim A. Osswald, Juan P. Hernandez-Oritz.- lsted. p. cm. 

In gratitude to Professor R.B. Bird, the teacher and the pioneer who laid the groundwork for polymer processing — modeling and simulation... 

The more complex this mathematical model, the more accurately it represents the actual process. Eventually, the complexity is so high that we must resort to numerical simulation to model the process, or often the model is so complex that even numerical simulation fails to deliver a solution. Chapters 5 and 6 of this book address how mathematical models are used to represent polymer processes using analytical solutions. Chapters 7 to 11 present various numerical techniques used to solve more complex polymer processing models. 

M. Miyazaki, M. Yamaura, T. Takayama, S. Kihara, and K. Funatsu, 3-D Flow Simulation of Shielding Disk in Twin Screw Extruders, Proc. 16th Ann. Meet. Polym. Process. Soc., Shanghai, China, 2000, pp. 268-269. 

Fig. 12.16 Entrance flow patterns in molten polymers, (a) Schematic representation of the wine glass and entrance vortex regions with the entrance angle. [Reprinted by permission from J. L. White, Critique on Flow Patterns in Polymer Fluids at the Entrance of a Die and Instabilities Leading to Extrudate Distortion, App/. Polym. Symp., No. 20, 155 (1973).] (b) Birefringence entrance flow pattern for a PS melt. [Reprinted by permission from J. F. Agassant, et al., The Matching of Experimental Polymer Processing Flows to Viscoelastic Numerical Simulation, Int. Polym. Process., 17, 3 (2002).]...

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