Numerical Simulation of Contraction Flows for Boger Fluids using Finite Volume Methods

نویسندگان

  • M. Aboubacar
  • T. N Phillips
  • H. R. Tamaddon-Jahromi
  • M. F. Webster
  • A. J. Williams
چکیده

INTRODUCTION Simulation of constant-viscosity memory-fluids flows is undertaken, considering single-mode differential models and two different numerical schemes. Comparisons are performed against experimental observations, for pressure drop (∆P ) and vortex cell-size (X). We interpret such issues through increasing flow-rate for a given fluid. Tests have demonstrated that this is equivalent to increasing relaxation time, throughout the creeping flow regime. To this end, we consider high and low solvent-fractions for Oldroyd-B models to approximate Boger fluids. Flows under consideration include planar and axisymmetric, abrupt, 4:1 geometric ratio, contraction flows. A series of meshes have been considered, covering triangular unstructured and rectangular structured forms. Numerical techniques employed are time-stepping algorithms, one of hybrid finite element/volume (fe/fv [1]) type, the other of pure finite volume form (SLFV2 [4]). In the former, a Taylor-Galerkin/pressure-correction finite element discretisation is used to solve for continuity and momentum balance equations, in combination with a second-order cell-vertex scheme for stress. Such a scheme has been developed for unstructured triangular meshes, that appeals to both fluctuation distribution and median-dual-cell nodal update contributions. The pure finite volume scheme is a staggeredgrid cell-centred-scheme, applied on rectangles (structured meshes). In this formulation the convection terms are treated in a semi-Lagrangian fashion, which has the effect of stabilising the calculations. The system of algebraic equations at each time step is solved using the SIMPLER methodology.

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تاریخ انتشار 2002