Numerical simulation of the planar contraction flow of a Giesekus fluid
type: Item
instance of: scholarly article
title: Numerical simulation of the planar contraction flow of a Giesekus fluid
zbMATH Open document ID: 0669.76017
DOI: 10.1016/0377-0257(88)85061-4
author: Haecheon Choi
author: J. Y. Yoo
author: Jin H. Song
published in: Journal of Non-Newtonian Fluid Mechanics
publication date: 1988-01-01T00:00:00Z
review text: Finite difference calculation of a planar 4:1 contraction flow of the Leonov-like fluid (i.e., the 1-mode Giesekus model with mobility parameter \(\alpha =)\) has been performed on a non-uniform grid system. In discretizing the constitutive equations, an upwind corrected scheme involving an artificial viscosity term is introduced to attain second- order accuracy and unconditional stability, so that the whole system of the governing equations and the boundary conditions can be made second- order accurate for creeping flow, and nearly so for small Reynolds number flows. In the case of creeping flow, the numerical convergence and stability can be obtained up to higher values of the Weissenberg number, compared with those obtained by discretizing the constitutive equations with a simple upwind difference scheme on a uniform grid system. As the Weissenberg number increases, the corner vortex growth and the percent axial velocity overshoot along the center plane increase, which agrees qualitatively well with extant flow visualization and velocity measurement experiments using shear-thinning fluids. Besides, the distributions of the first normal stress difference for large Weissenberg number flows in the narrow channel exhibit qualitatively similar patterns as observed in existing flow birefringence experiments. For non-vanishing Reynolds number flows, it has been predicted that, as the flow rate, i.e., the viscoelastic Mach number, increases the corner vortex growth will decrease for small elasticity number fluid and increase for large elasticity number fluid.
Mathematics Subject Classification ID: 76A05
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 4096928
zbMATH Keywords: Finite difference calculation
zbMATH Keywords: Leonov-like fluid
zbMATH Keywords: non-uniform grid system
zbMATH Keywords: upwind corrected scheme
zbMATH Keywords: artificial viscosity
zbMATH Keywords: second-order accuracy
zbMATH Keywords: unconditional stability
zbMATH Keywords: creeping flow
MaRDI profile type: Publication
full work available at URL: 0377-0257(88)85061-4
OpenAlex ID: W2020948339
description: scientific article; zbMATH DE number 4096928