Simulation of Planar Entrance Flow Using Strain-Rate-Dependent Shear and Elongational Viscosities

A finite element simulation of the flow in a planar channel with an abrupt contraction is presented. The effect of the elongational viscosity of a polymer on the entrance flow is analyzed employing a truncated power-law model. The power-law index and the strain rate characterizing the transition from Newtonian to power-law behavior for the elongational viscosity are treated as being independent of the values of these two parameters for the shear viscosity. The effect of flow rate on planar entrance flow is also analyzed. It is confirmed that Trouton ratio is important in determining the recirculating vortex and the extra pressure loss in entrance flow. Extra pressure loss and vortex length predicted by a finite element simulation of a planar entrance loss are compared with the corresponding predictions from Binding’s approximate analysis.