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Abstract

This paper reviews both experimental and numerical studies of axisymmetric and planar entry flows, which have been considered as test problems for the numerical simulation of viscoelastic fluids. The test of the method is usually based upon whether the numerical model predicts vortices in the entry corners. However, it is not clear as to whether one should these vortices for viscoelastic fluids. Polyacrylamide solutions and Boger fluids exhibit vortices in axisymmetric contractions and the size of the vortex increases with fluid elasticity. However, the vortex is nearly suppressed in planar entry flow. On the other hand, not all polymer melts are fount to show vortices in either asixymmetric or planar entry flow. It is our belief that the origin of vortices is not related to the elasticity based on the shear properties but to the behaviour of the transient extensional viscosity. Certain polymer melts such as low density polyethylene exhibit vortices in both planar and axisymmetric contractions along with unbounded stress growth at the start up of extensional flow. It is believed that the constitutive equations used in the numerical simulation must reflect this extensional behaviour if vortices are to be predicted. On the other hand, a review of the numerical simulations concerned with entry flow shows that there is considerable doubt about the accuracy of the predictions for most of the studies. Even for those where the numerical solution is thought to be accurate, the magnitude of the stream function associated with the vortices is usually very low. None of the differential models used to date predicts strain hardening extensional viscosity, but those which are thought to predict vortices do rise more rapidly to the steady state extensional viscosity values with time. It is recommended that the search of test fluids be widened beyond polymer solutions, as there may already exist a number of polymer melts, which behave similarly to the predictions of existing constitutive equations.

J.Non-Newt.Fl.Mech. 24, 121-160, 1987

Review of the entry flow problem: experimental and numerical