NUMERICAL-SIMULATION OF PLANAR ENTRY FLOW FOR A POLYISOBUTYLENE SOLUTION USING AN INTEGRAL CONSTITUTIVE EQUATION

Numerical simulations have been undertaken for the entry flow through a 4:1 planar contraction of a well-characterized shear-thinning polymer solution (polyisobutylene in tetradecane) used previously in an experimental study. The fluid has been modeled using an integral constitutive equation of the K-BKZ type with a spectrum of four relaxation times. Numerical values for the constants appearing in the equation have been obtained from fitting linear viscoelastic material functions as well as shear and elongational viscosity data and normal stresses as measured in shear. The numerical solutions for the range of experimental Deborah and Reynolds numbers show a stagnant small corner vortex that slightly decreases with increasing flow rate. The velocity and stress fields are compared with the experimental ones, showing a good general agreement. The constitutive equation overpredicts, however, the maximum centerline birefringence values by as much as 40% for the highest De. The behavior of shear stress and first normal stress difference near the re-entrant comer are also illustrated.