*Article* **An Effective Interface Tracking Method for Simulating the Extrudate Swell Phenomenon**

**Ahmad Fakhari <sup>1</sup> , Željko Tukovic 2,\*, Olga Sousa Carneiro <sup>1</sup> and Célio Fernandes <sup>1</sup>**


**Abstract:** The extrudate swell, i.e., the geometrical modifications that take place when the flowing material leaves the confined flow inside a channel and moves freely without the restrictions that are promoted by the walls, is a relevant phenomenon in several polymer processing techniques. For instance, in profile extrusion, the extrudate cross-section is subjected to a number of distortions that are motivated by the swell, which are very difficult to anticipate, especially for complex geometries. As happens in many industrial processes, numerical modelling might provide useful information to support design tasks, i.e., to allow for identifying the best strategy to compensate the changes promoted by the extrudate swell. This study reports the development of an improved interface tracking algorithm that employs the least-squares volume-to-point interpolation method for the grid movement. The formulation is enriched further with the consistent second-order time-accurate noniterative Pressure-Implicit with Splitting of Operators (PISO) algorithm, which allows for efficiently simulating free-surface flows. The accuracy and robustness of the proposed solver is illustrated through the simulation of the steady planar and asymmetric extrudate swell flows of Newtonian fluids. The role of inertia on the extrudate swell is studied, and the results that are obtained with the newly improved solver show good agreement with reference data that are found in the scientific literature.

**Keywords:** extrusion; extrudate swell; interface tracking; least-squares volume-to-point interpolation; consistent PISO; finite volume method; OpenFOAM
