Models/modeling polymer processing

In this chapter the general equations of laminar, non-Newtonian, non-isothermal, incompressible flow, commonly used to model polymer processing operations, are presented. Throughout this chapter, for the simplicity of presentation, vector notations are used and all of the equations are given in a fixed (stationary or Eulerian) coordinate system. 

The balance equations used to model polymer processes have, for the most part, first order derivatives in time, related with transient problems, and first and second order derivatives in space, related with convection and diffusive problems, respectively. Let us take the heat equation over an infinite domain as... 

In their recent review paper, Properly model polymer processes, Bokis et al. from Aspen list the polymer models currently supplied in the ASPEN-Plus Process Simulator ... 

Bokis, C., Orbey, H., and Chen C.-C., Properly model polymer processes, Chem. Eng. Progr., April, 39, 1999. 

Two-dimensional models can be used to provide effective approximations in the modelling of polymer processes if the flow field variations in the remaining (third) direction are small. In particular, in axisymraetric domains it may be possible to ignore the circumferential variations of the field unlaiowns and analytically integrate the flow equations in that direction to reduce the numerical model to a two-dimensional form. 

IMPOSITION OF BOUNDARY CONDITIONS IN POLYMER PROCESSING MODELS... 

Pittman, J. F. T., 1989. Finite elements for field problems. In Tucker, C. L. Ill (ed.), Computer Modeling for Polymer Processing, Chapter 6, Hanser Publishers, Munich, pp. 237- 331. 

As mentioned in Chapter 2, the numerical solution of the systems of algebraic equations is based on the general categories of direct or iterative procedures. In the finite element modelling of polymer processing problems the most frequently used methods are the direet methods. 

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. 

PRACTICAL ASPECTS OF FINITE ELEMENT MODELLING OF POLYMER PROCESSING... 

Finite element methods are one of several approximate numerical techniques available for the solution of engineering boundary value problems. Analysis of materials processing operations lead to equations of this type, and finite element methods have a number of advantages in modeling such processes. This document is intended as an overview of this technique, to include examples relevant to polymer processing technology. 

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. 

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