# Servicio de Información Comunitario sobre Investigación y Desarrollo - CORDIS

## Realistic mathematical models and numerical implementation in realistic processing conditions

The aim of the Work package 4 was to develop numerical tools for polymer processing. The first step was the development of specific model for the draw resonance and the spurt flow instabilities.

- Specific models.
-- The linear stability of the spinning process in non-isothermal conditions has been studied. This model allows determining the critical draw ratio for the onset of the draw resonance instability. The influence of cooling due to convective exchange with air and different mechanical behaviour for the molten polymer are considered in this model.

-- The model for the spurt flow instability assumes both compressibility in the reservoir and slip at the wall (in the capillary) above a critical shear stress. A complex stick-slip mechanism at the wall allows predicting stable and unstable flows. Strong hypothesis on the flow geometry are used for these two models and it results in efficient and relatively easy to use numerical codes. These tools are fitted for the analysis of laboratory experiments. The price to pay for this simplicity is the difficulty to consider more complex flows encountered in industrial process. These models of the first generation were completed by a more complex to use but more adjustable finite element code.

- General models. The second task of Work package 4 was to develop general numerical tools allowing to compute numerically polymer flow obeying a generalized Newtonian (Carreau-Yasuda) or a viscoelastic (multi-mode Phan-Tien Tanner or multi-mode Pom-Pom model) behavior. We have used the general framework of the finite element code MEF++ (version 2.0) developed by the GIREF at the Laval University in Québec (Canada). It can be used to compute numerical problems in solids and fluids mechanics, heat transfer and coupled problems (see for example http: //www.giref.ulaval.ca). Specific modules was developed for the computation of molten polymer flow obeying realistic constitutive equations. These modules can now be used as bricks to built models for realistic geometries. This code uses classically balance and constitutive equations and boundaries conditions. It leads to a complex set of non linear equations solved using iterative techniques.

The important steps are the following:
- Meshing of the flow geometry,
- Choose of a numerical path,
- Iterations until convergence.

It is necessary to precise that each of these steps requires some knowledge in numerical computations.

- Conclusion. The numerical modules necessary for the study of the stability of polymer flows in industrial geometries are available. These modulus have been used to study the helical instability (C. Combeaud, CEMEF) and the flow in the Multipass Rheometer (R. Valette, Cambridge).