How to Apply Carreau´s Approach without CFD-Tools

Constitutive equations like those of Carreau, Cross and Yasuda allow an accurate description of the flow behavior of polymeric melts. In combination with approaches like that of Arrhenius or Williams-Landel-Ferry (WLF), the viscosity can be described as a function of the shear rate, temperature, and pressure. These equations are often not applied, since not even the flow behavior in simple, one-dimensional geometries such as slit, round hole or circular ring nozzles can be determined analytically. Often those approaches are not even realized in commercially available computational fluid dynamics (CFD) tools.
This work deals with the 1-dimensional modeling and simulation of the viscous flow of polymers in flat film, round hole and circular ring nozzles considering those realistic constitutive equations, the pressure and temperature dependence of the polymeric melt and difficult boundary conditions like moving wall conditions (e. g. coating of sheets or cables). The work shows how this simulation can be done using standard spreadsheet software. Furthermore, an easy-to-use spreadsheed file will be provided. This file can be used to determine both the throughput as a function of pressure and the pressure required to achieve a predefined throughput.