Flow of a curtiss-bird fluid over a transverse slot using the finite element drift-function method

Abstract

A finite element method for incompressible flows of a memory fluid is described which is based on macroelements of crossed linear triangels. This allows virtually exact computations of strains in trial velocity fields. Memory is handled by construction of special Gaussian quadrature formulas. The problem of plane flows over slots is studied numerically using the reptational constitutive equation proposed by Curtiss and Bird. With this constitutive equation and an improved nonlinear iteration scheme, convergence difficulties which plagued earlier attempts at modelling viscoelastic flow seem to be avoided. Particular attention is paid to the relationship between first normal-stress difference and pressure difference across the slot as a function of Deborah and Reynolds number. The model predicts that there is a strong correlation between hole-pressure and first normal-stress difference if the inertial contribution to the hole-pressure is accounted for. Nevertheless the correlation differs to some extent from the Higashitani-Pritchard prediction. In our model this is traceable to specific violations of Higashitani and Pritchard's assumptions related to fluid-memory effects.