Numerical optimization of planar nozzle shapes for fused deposition modeling

Purpose In fused deposition modeling (FDM), the nozzle plays a critical role in enabling high printing speeds while maintaining precision. Despite its importance, most applications still rely on standard nozzle designs. This paper aims to investigate the influence of nozzle geometry on pressure loss inside the nozzle, a key factor in high-speed printing performance. Design/methodology/approach The authors focus on optimizing the nozzle shape to minimize the pressure loss and establish a framework that allows both simple angle-based optimization and more advanced spline-based parametrization. To model the polymer melt flow, the authors use a Giesekus model to account for viscoelastic effects. Findings For angle-based optimization, the pressure-loss objective exhibits two local minima: one associated with smooth flow and another with pronounced recirculation regions inside the nozzle. While the latter yields a lower pressure drop, such flow patterns are generally undesirable due to increased residence times and the associated risk of material degradation and nozzle clogging. The spline-based parametrization results in only marginal additional reductions in pressure loss compared to angle optimization, while decreasing the manufacturability of the nozzle considerably. Originality/value This paper presents a comparative study of FDM nozzle shape optimization using a Giesekus model. The authors introduce a flexible optimization framework that accommodates both simple and advanced geometric parametrizations. The main contribution is the systematic comparison between angle- and spline-based parametrizations across materials and extrusion velocities, showing that most of the achievable pressure-loss reduction is already captured by the simpler and more manufacture-ready angle optimization.