Optimizing die profiles using a hybrid optimization algorithm for the precise control of extrudate swell in polymer solutions

In recent years, many researchers have focused on improving the die design process for polymer extrusion. This study proposes the development of an efficient and robust numerical approach to improve the die-designing process of polymer melts using the Giesekus model. The proposed technique uses a hybrid optimization algorithm to systematically minimize an objective function to achieve the desired extrudate shape. First, we examine the proposed objective function for the 2D axisymmetric test case using the Golden Section optimization algorithm to obtain a circular extrudate of high-density polyethylene (HDPE) with the desired radius at moderate Weissenberg numbers from 1 to 3.75. To provide more insights into the viscoelastic nature of the problem, the optimization was repeated for a viscoelastic fluid with a higher viscosity ratio and a lower mobility factor at very high Weissenberg numbers, specifically 45, 60, 75, and 90. The proposed approach performs quite well across a broad range of Weissenberg numbers. Subsequently, a hybrid optimization algorithm that combines Nelder-Mead and Bayesian optimization algorithms is employed to achieve the desired extrudate shape for various extrudate profiles in 3D cases, including rectangular and square cross-sections, at a Weissenberg number of one. To gain additional insights into the viscoelastic nature of the problem, optimization was conducted for the rectangular extrudate with a 2:1 aspect ratio at higher Weissenberg numbers, i.e. Weissenberg number from 1 to 2.6. The results of the three-dimensional case studies indicate that both the Nelder-Mead and Bayesian optimization algorithms are efficient and robust, converging relatively quickly in all cases studied. The Nelder-Mead algorithm appears to be more robust, exhibiting fewer oscillations when reaching the optimum point. On the other hand, the Bayesian optimization algorithm can reach the global optimum point at a computational cost comparable to Nelder-Mead, while achieving greater accuracy. In conclusion, these findings indicates that using this hybrid optimization algorithm in the polymer extrusion die-designing process can provide a high level of efficiency and robustness.