On the combined effects of slip, compressibility, and inertia on the Newtonian extrudate-swell flow problem

Abstract

We solve both the planar and axisymmetric extrudate-swell flows of a compressible Newtonian liquid with Navier slip at the wall, using the finite-element method in space and a fully-implicit finite-difference scheme in time. Our aim is to investigate the combined effects of compressibility, slip, and inertia on the shape of the extrudate and the extra pressure losses in the system (exit correction factor). The numerical simulations show that compressibility at moderate and higher Reynolds numbers results in stable steady-state solutions in which the extrudate surface is wavy, especially just after the die exit. The stability of these oscillatory steady-states is investigated by means of time-dependent calculations. At moderate Reynolds and slip numbers, interesting oscillatory extrudate shapes are observed due to the fact that slip tends to reduce the extrudate contraction opposing the inertia effect. The final extrudate swell ratios obtained at high Reynolds numbers and various slip numbers agree well with the theoretical asymptotic values for the case of incompressible flow.