Accurate determination of a deformation measure in the screw extrusion process

It is important to evaluate the deformation process accurately in analyzing mixing in extrusion. This paper discusses numerical methods to determine a representative deformation measure over the entire cross-section of the extruder channel accurately and efficiently. Two different numerical methods are introduced to determine a deformation measure over the entire cross-section of the extruder channel efficiently: i) the first method based on the mapping sequence of the deformation gradient tensor; and ii) the second method which does not require the evaluation of velocity gradient fields. These two methods are applied to the extrusion process of a single-screw extruder and are compared with respect to their numerical accuracy. It is found that trajectories of fluid particles are difficult to obtain especially near the screw flight and barrel surface, which causes numerical inaccuracies with respect to obtaining a deformation measure. In this paper an inverse mapping method is employed to overcome such a numerical problem. For computational efficiency and accuracy, the second method was found to be more powerful compared with the first one, especially when there are singular points as in an extruder channel.