Numerical verification of sharp corner behavior for Giesekus and Phan-Thien-Tanner fluids

J. D. Evans, I. L. Palhares Junior, C. M. Oishi, F. Ruano Neto

Research output: Contribution to journalArticlepeer-review

Abstract

We verify numerically the theoretical stress singularities for two viscoelastic models that occur at sharp corners. The models considered are the Giesekus and Phan-Thien-Tanner (PTT), both of which are shear thinning and are able to capture realistic polymer behaviors. The theoretical asymptotic behavior of these two models at sharp corners has previously been found to involve an integrable solvent and polymer elastic stress singularity, along with narrow elastic stress boundary layers at the walls of the corner. We demonstrate here the validity of these theoretical results through numerical simulation of the classical contraction flow and analyzing the 270 ° corner. Numerical results are presented, verifying both the solvent and polymer stress singularities, as well as the dominant terms in the constitutive equations supporting the elastic boundary layer structures. For comparison at Weissenberg order one, we consider both the Cartesian stress formulation and the alternative natural stress formulation of the viscoelastic constitutive equations. Numerically, it is shown that the natural stress formulation gives increased accuracy and convergence behavior at the stress singularity and, moreover, encounters no upper Weissenberg number limitation in the global flow simulation for sufficiently large solvent viscosity fraction. The numerical simulations with the Cartesian stress formulation cannot reach such high Weissenberg numbers and run into convergence failure associated with the so-called high Weissenberg number problem.

Original languageEnglish
Article number113106
JournalPhysics of Fluids
Volume34
Issue number11
Early online date4 Nov 2022
DOIs
Publication statusPublished - 30 Nov 2022

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

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