Semi-analytical models for non-Newtonian fluids in tapered and cylindrical ducts, applied to the extrusion-based additive manufacturing. (November 2022) - Pricci, Alessio; Tullio, Marco D. de; Percoco, Gianluca
Graphical abstract: Highlights: A fast iterative method for the description of the flow of both Cross-WLF and Carreau fluids in straight nozzles shows higher accuracy if compared to analytical methods. The flow of Cross-WLF and Carreau fluids in converging nozzles can be predicted calculated by means of the Jeffery-Hamel flow approximation, especially at very low taper angles and flow rates. This theory has been applied to additive manufacturing; in particular, the extrusion of moisture-cured silicones (Carreau) and molten thermoplastic materials (Cross-WLF) has been analysed. Abstract: In this paper, mathematical models aiming at describing the fluid flow of non-Newtonian fluids inside ducts with both convergent and cylindrical sections have been formulated. The theory has been implemented for the description of industrially interesting fluids such as moisture-cured silicones and thermoplastics, which are well described by the Carreau and Cross-Williams-Landel-Ferry (Cross-WLF) rheological models, respectively. The viscous flow in a die has been considered, comparing the results with Computational Fluid Dynamics (CFD) solutions extracted through the Finite Element Method (FEM) software Comsol Multiphysics. The agreement with numerical data is very good, showing the potential for next experimental applications in predicting some very important and useful quantities, such as the extrusion force, which is critical for a wide range of 3D printing processes. The novelty relies in the general applicability of the theoretical models to viscous flows, no matter what its rheological behaviour is.