Abstract
Numerical simulations have been undertaken for the entry flow of a well-characterized polymer solution (fluid M1) through 4:1 and 22:1 circular contractions. The fluid has been modelled using an integral consti- tutive 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 and elongational viscosity data and normal stresses as measured in shear. The numerical solutions show that vortex growth occurs in a 4:1 circular contraction in agreement with experimental results for low to moderate shear rates. However, for high shear rates the simulations show a continuing increase in vortex size (but not in intensity), while experiments show a gradual elimination of the vortex even if the Reynolds number is less than one. In contrast, flow in a 22:1 circular contraction exhibits a vortex growth always in agreement with experimental observations. The present results show that geometry and inertia effects play an important role in the flow of viscoelastic fluids through contractions and should not be neglected in the simulations.
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