SPATIAL DECAY OF STEADY PERTURBATIONS OF PLANE POISEUILLE FLOW FOR THE OLDROYD-B EQUATION

A numerical eigenfunction analysis of steady perturbations of plane Po iseuille flow for the Oldroyd-B equation is presented. From this the i mportance of the downstream boundary conditions used in entry-flow cal culations may be determined. It is shown that the length scale over wh ich the downstream boundary condition affects the upstream flow is muc h shorter than the length scale over which the polymer stress relaxes to that of fully developed flow. Consequently features such as vortex enhancement should not be significantly affected by the downstream bou ndary condition. A correction to the pressure drop is also derived, th ereby allowing the Couette correction to be calculated even when the d ownstream section is too short for fully developed flow to be obtained at the downstream boundary of the computational domain. In addition w e show that an instability criterion for time-dependent simulation of planar Couette flow derived in an earlier paper (R.A. Keiller, J. Non- Newtonian Fluid Mech., 43.(1992) 229-246) may also apply to steady-sta te calculations of Poiseuille flow.