On the flow of a polymer melt passing over a transverse slot

The phenomenon of hole pressure occurs whenever a polymeric or viscoelastic liquid flows over a depression in a conduit wall. Numerical simulations un dertaken for the flow of an aqueous polyacrylamide melt passing over a tran sverse slot are considered here. The fluid model used for this study is a W hite-Metzner constitutive equation describing the non-Newtonian behavior of the melt. The results were computed by an elastic-viscous split-stress fin ite element method (EVSS-FEM), a mixed finite element method incorporating the non-consistent streamline upwind scheme. For verification, the numerica l algorithm was first applied to compute the corresponding flow of the uppe r-convected Martwell fluid model, a special case of the White-Metzner model characterized by constant viscosity and relation time. The resulting hole pressure (P-h) was evaluated for various Deborah numbers (De) and compared with the analytical prediction derived from the Higashitani-Pritchard (HP) theory. The agreement was found to be satisfactory for creeping flow in the low De range, for which the HP theory is valid. Subsequently, the hole pre ssure of this flow problem was predicted. The streamlines and pressure dist ribution along the channel walls are also presented. Furthermore, the effec ts of fluid elasticity, shear thinning, the exponent in the viscosity funct ion and the relaxation-time function, and slot geometry on the hole pressur e were investigated.