Models polymer melt flows

Since a standard screw geometry within a cooling extruder has a periodic flow chaimel, a periodic inflow/outflow boundary condition is applied to simulate fully developed flow. Validation tests showed that a single pitch of the screw with poiodic boundary conditions is sufficient to model polymer melt flow behavior in the whole cooling screw geometry. 

One of the common problems associated with underwater pelletizers is the tendency of the die holes to freeze off. This results in nonuniform polymer melt flow, increased pressure drop, and irregular extrudate shape. A detailed engineering analysis of pelletizers is performed which accounts for the complex interaction between the fluid mechanics and heat transfer processes in a single die hole. The pelletizer model is solved numerically to obtain velocity, temperature, and pressure profiles. Effect of operating conditions, and polymer rheology on die performance is evaluated and discussed. 

The flow properties of the polymer must be matched to the mold (or vice versa) in order to achieve optimum product quality. In particular, we must manage the pressure drop between the gate and the furthest extent of the flow path. Articles with thin walls, such as margarine tubs, require low viscosity resins. In other cases, the situation is more complex and the cavity may need to be designed so that the product is thicker near the gate than it is at its extremities. The development of complex products is aided by computer modeling of melt flow within the mold cavity. 

This paper describes a finite element formulation designed to simulate polymer melt flows in which both conductive and convective heat transfer may be important, and illustrates the numerical model by means of computer experiments using Newtonian extruder drag flow and entry flow as trial problems. Fluid incompressibility is enforced by a penalty treatment of the element pressures, and the thermal convective transport is modeled by conventional Galerkin and optimal upwind treatments. 

Development of this model is continuing in our laboratory, and among the aspects still under development are capabilities for transient flows, reactive fluids, free surfaces, and wall slip. Although incorporation of fluid elasticity is desired due to its importance in many polymer melt flows, such a development has proven elusive to a number of well qualified groups in the past several years. At present, it seems prudent to let the theoretical aspects of elastic effects be developed further before attempting their incorporation in a general process model. 

Verbeeten WMH, Peters GWM, Baaijens FPT (2001) Differential constitutive equations for polymer melts The extended Pom-Pom model. J Rheol 45 823-843 Verbeeten WMH, Peters GWM, Baaijens FPT (2002) Viscoelastic analysis of complex polymer melt flows using the extended Pom-Pom model. J Non-Newtonian Fluid Mech 108 301-326 Verleye V, Dupret F (1993) Prediction of fiber orientation in complex injection molded parts. 

FDM technology has continued to evolve with significant advances in three fields. First, researchers recognized that process and product performance can be improved with negligible added cost by implementing control algorithms that incorporate mechanistic models of the process dynamics. One example [15] concurrently controls the filament drive and head traversal velocity by a move-compiler that considers the dynamics of the polymer melt flow. Specifically, the filament is overdriven to minimize... 

Verbeeten, W. M. H., Peters, G. W. M., Baaijens, F. P. T. Viscoelastic analysis of complex polymer melt flows using the Extended pom-pom model. /. Non-Newt. Fluid Mech. (2002) 108, pp. 301-326... 

Fig. 5.6 Flow in an Annular Slot 5.4 Rheological Models for Polymer Melt Flow...

In the study, the mathematical model of the polymer melt flows in the extrusion process of plastic profile with metal insert was developed and the complex melt rheological behavior was simulated based on the finite element method. The melt flow characteristic in the flow channel was analyzed. The variation of the melt pressure, velocity, viscosity and stress versus different metal insert moving rate was investigated. Some suggestions on its practical manufacturing control were concluded based on the simulation results. 

MATHEMATICAL MODEL AND NUMERICAL ANALYSIS OF POLYMER MELT FLOW AND HEAT TRANSFER IN A COOLING EXTRUDER... 

This paper presents a mathematical model and numerical analysis of momentum transport and heat transfer of polymer melt flow in a standard cooling extruder. The finite element method is used to solve the three-dimensional Navier-Stokes equations based on a moving barrel formulation a semi-Lagrangian approach based on an operator-splitting technique is used to solve the heat transfer advection-diffusion equation. A periodic boundary condition is applied to model fully developed flow. The effects of polymer properties on melt flow behavior, and the additional effects of considering heat transfer, are presented. 

Chapter 5 deals with the aspects of the flow behaviour of polymer melts which are relevant to the processing methods. The models are developed for both Newtonian and Non-Newtonian (Power Law) fluids so that the results can be directly compared. 

Chapter 4 describes in general terms the processing methods which can be used for plastics and wherever possible the quantitative aspects are stressed. In most cases a simple Newtonian model of each of the processes is developed so that the approach taken to the analysis of plastics processing is not concealed by mathematical complexity. Chapter 5 deals with the aspects of the flow behaviour of polymer melts which are relevant to the processing methods. The models are developed for both Newtonian and Non-Newtonian (Power Law) fluids so that the results can be directly compared. 

Some of these questions have strict and unambiguous answers, in a mathematical model, to other answers are derived from extensive empirical material. The present paper will discuss the problems formulated above, but concerning only rheological properties of filled polymer melts, leaving out the discussion of specific hydrodynamic effects occurring during their flow in channels of different geometrical form. 

The hydromechanics of flows of gas-containing polymer melts is extremely complicated to analyse and describe mathematically. Nevertheless, comprehensive experimental investigations in this sphere have yielded simple models of unidimensional flows, and solved several problems pertaining to the physics and hydromechanics of complex medium flows. 

In the past three decades, industrial polymerization research and development aimed at controlling average polymer properties such as molecular weight averages, melt flow index and copolymer composition. These properties were modeled using either first principle models or empirical models represented by differential equations or statistical model equations. However, recent advances in polymerization chemistry, polymerization catalysis, polymer characterization techniques, and computational tools are making the molecular level design and control of polymer microstructure a reality. 

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