Die swell measurements of second-order fluids: numerical experiments

Abstract

An analysis of the flow of a second‐order fluid is presented. Reference values for some variables are defined, and with these a non‐dimensional formulation of the governing equations. From this formulation, three dimensionless numbers appear; one is the Reynolds number, and two numbers that are called the first‐ and second‐dimensionless normal stress (NSD) coefficients. The equations of motion are solved by a finite element method using a commercially available program (Fidap), and the steady state converged solution was used to measure the die swell. The factors that influence die swell and that are studied in this work include: the die geometry for circular cross sectional dies, including tubular, converging, diverging, half‐converging/half‐tubular shapes; fluid characteristics such as Reynolds number and first‐ and second‐DNS coefficients (both positive and negative values); and flow rates, as determined by the maximum velocity in a parabolic velocity profile at the entrance to the die. The results suggest that shear and deformation histories of the fluid directly influence not only swell characteristics, but also convergence characteristics of the numerical simulation. © 1999 John Wiley & Sons, Ltd.

Modeling of bubble growth dynamics and nonisothermal expansion in starch‐based foams during extrusion

“…A similar mechanism for die swell of viscoelastic fluids has been reported previously. [17][18][19] Bubble Growth Figure 5 gives the bubble radius, domain radius, and thickness of bubble shell versus axial distance of extrudate. The bubble radius increased very slowly near the die exit and very rapidly toward the end of expansion.…”

“…[10][11][12][13][14][15][16] Furthermore, when the melt emerges from the die channel, the viscous effects of the viscoelastic melt also cause die swell, increasing the diameter of the extrudate. [17][18][19] Therefore, both bubble growth and die swell contribute to the expansion mechanism of starch-based foams.…”

Application of the PTT Model for Capillary Extrusion of Rubber Compounds

“…In profile extrusion, the parameters mentioned above affect the extrudate profile and the prediction of the extrudate profile is not easy. Computer simulations of profile extrusion have been published in the papers using numerical simulations (Huang and Leong, 2002;Gifford, 1998;Tokita, 1981;Ngamaramvaranggul and Webster, 2001;Gast and Ellingson, 1999;Müllner et al, 2006;Montes and White, 1993). Most of the published studies for profile extrusion were focused on the numerical scheme and geometry of die.…”

Solução Numérica de escoamentos viscoelásticos tridimensionais com superfícies livres: fluidos de segunda ordem

“…Entre os trabalhos que simulam escoamentos com superfície livre utilizando essa equação constitutiva, podemos mencionar o trabalho de Gast e Ellington [31] que utilizaram o código FIDAP [30] para simular o inchamento do extrudado de um Fluido de Segunda Ordem e conseguiram resultados para uidos com pouca elasticidade (isto é, número de Deborah pequeno, De ≈ 0.1). Mais recentemente, Tomé et al [13] apresentaram um método numérico para simular escoamentos com superfícies livres governados pela equação constitutiva Fluidos de Segunda Ordem em duas dimensões.…”