Numerical simulation of entry flow of fluid S1

Abstract

Numerical simulations have been undertaken for the creeping flow of a well-characterized polymer solution (fluid S1) in the benchmark problem of the entry flow in a 4:1 axisymmetric contraction. The fluid has been modelled using an integral constitutive equation of the K-BKZ type with a spectrum of relaxation times. Numerical values for the constants appearing in the equation have been obtained from fitting shear viscosity and normal stress data as measured in shear, and elongational viscosities both steady-state and transient. Convergence of the numerical scheme was obtained for the whole range of experiments previously performed by Byars et al., J. Non-Newtonian Fluid Mech. 72 (1997) 219–235. The numerical solutions show that the vortex in the reservoir increases monotonically with increasing flow rate (or Weissenberg number) in agreement with the experiments. For identical flow conditions, a sudden contraction shows a higher vortex growth than a contraction with a rounded re-entrant corner, again in agreement with experiments.