Re-entrant corner flow for PTT fluids in the natural stress basis

Jonathan D Evans, David N Sibley

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We revisit the situation of steady planar flow of Phan–Thien–Tanner (PTT) fluids around re-entrant corners of angles π/α where 1/2 ≤ α < 1. The model is considered in the absence of a solvent viscosity, under which a class of self-similar solutions has been identified with stress singularities of O(r−2(1− α )) and stream function behaviour O(r α (1+ α)) (r being the radial distance from the corner). The asymptotic analysis is completed by providing a solution for the downstream boundary layer using natural stress variables. We show that the matching of the outer (core) solution into the downstream boundary layer imposes a restriction on the range of α ε (2/3, 1) for which these self-similar solutions are applicable, i.e. they only hold for corner angles between 180◦ and 270◦.
Original languageEnglish
Pages (from-to)79-91
Number of pages13
JournalJournal of Non-Newtonian Fluid Mechanics
Volume157
Issue number1-2
DOIs
Publication statusPublished - 2009

Keywords

  • Phan-Thien-Tanner (PTT)
  • Boundary layers
  • Self-similar solutions
  • Natural stress basis
  • Stress singularity
  • Re-entrant corner

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