ENTRY-FLOW CALCULATIONS FOR THE OLDROYD-B AND FENE EQUATIONS

Entry-flow calculations are presented for the Oldroyd-B and FENE equat ions in the limit of high contraction ratio in both planar and axisymm etric geometries. In addition to abrupt entry flow a cone-shaped entry flow of half-angle pi/4 is also considered. A decoupled finite-differ ence scheme is used with time stepping to converge to the solution of the non-linear equations. For the solution of the stress equation a st reamline integration technique is developed. For the FENE equation it is found that a reordering of the elliptic operator for the stream fun ction enables larger time steps to be taken at high We when the polyme rs are near full extension. These calculations show that the FENE equa tion can predict much larger vortices than the Oldroyd-B equation when in the non-linear regime of the FENE spring. No vortices are observed for the Oldroyd-B equation in planar flow and only weak vortices when the flow is axisymmetric. For the cone entry flow, larger vortices ar e again predicted for the FENE equation but they remain localised near the entry, in a manner similar to lip vortices. Pressure drops are al so considered and it is argued that at high We the non-dimensional dec rease in pressure drop compared with the Newtonian pressure drop shoul d be linear in We for the Oldroyd-B equation. An estimate of this pres sure drop is made in the high We, but low concentration, limits.