Theoretical and numerical studies of die swell flow

Abstract

This paper focuses on the theoretical and numerical predictions of die-swell flow for viscoelastic and viscoelastoplastic fluids. The theoretical results on die swell have been obtained by Tanner for a wide class of constitutive equations, including Phan-Thien Tanner (PTT), pom-pom, and general network type models. These results are compared with numerical solutions across swelling ratio, pressure drop, state of stress, and dissipation-rate for two fluid models, exponential Phan-Thien Tanner (EPTT) and Papanastasiou-Exponential Phan-Thien Tanner (Pap-EPTT). Numerically, the momentum and continuity flow equations are solved by a semi-implicit time-stepping Taylor-Galerkin/pressure-correction finite element method, whilst the constitutive equation is dealt with by a cell-vertex finite volume (cv/fv) algorithm. This hybrid scheme is performed in a coupled fashion on the nonlinear differential equation system using discrete subcell technology on a triangular tessellation. The hyperbolic aspects of the constitutive equation are addressed discretely through upwind fluctuation distribution techniques.